WOW. There's a lot of awesome advice in this thread, and I wanted to add my two cents in. My table's Crash Bang Labs, and I've been doing Artist Alleys since around 2002, and I think I've been vending at ACen since around 2006 - if my number of badges I have saved up is correct.

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I also apologize for adding a wall of text here...
A lot of the obvious has been covered, so I won't necessarily rehash that (like table prices, etc), but I did want to add some advice from my own experience.
What is the average amount of merchandise you have on your table? (Small cons & larger cons)
My strongest recommendation is to fill your space to the best you can. If your booth looks "empty" people will not want to come up to your booth to look at it. The less empty space you have showing, the better. (I'm going to put some further merch advice down at the bottom of the post too)
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For those who have been in Artist Alley, what of your merchandise usually sells the best? (stickers, posters, paintings, calendar, pins, keychains, buttons, etc)
This will actually vary from year to year. When I started it was prints and bookmarks. Then it was buttons. Then charms/keychains. Intermixed in there it also added in "items" like beadspriting which took off around 4 or 5 years ago (there were TONS of bead spriters), then it was fleece hats, then amigurumi.
I just got back from Katsucon not too long ago, and discovered that prints were big again (at least on the east coast. I'm going to Shutocon in April, so I want to do some more observation to see if the theory holds.
Truthfully, I suggest walking through artists alleys of any con you go to prior to vending at any (I still do this). Look at what the stalls have. Take business cards. Look at what people are carrying in their hands.
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How do you make sure that you profit from a table and not lose out on money? Have you ever lost profit on a table?
Like everybody else said: BUDGET BUDGET BUDGET. Make a little excel sheet of everything you buy to see just how much it costs you, and in the long run, this will help you price your products too.
For your very first alley, you will most likely be lucky to break even. Between the initial set up of the booth (table cloth/display, print costs, manufacturing, buying your supplies, cash box, etc) and things like convention costs, hotel costs, and gas, breaking even on a first con is FABULOUS. After that, your stock is built up and you just have to keep adding new things, and "retiring" old products.
I actually just barely broke above even at Katsucon this year, and I blame the VERY expensive hotel. I'd love to go back there, but I'm looking for less expensive housing.
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How do you know how much merch you should purchase/How much should you purchase depending on the con? (small cons & larger)
This comes from experience, unfortunately. It also depends on if you're doing other conventions or having an online shop after. I live by the thoughts of "better too much than not enough", and as you do more cons you figure out what's a good amount of stock to keep on hand. Some products are easier to keep on hand than others (and will depend on how you store them).
Example: I have little cell phone charms. I bought one of those cases with smaller cases in it in the scrapbooking area (
Large Photo Keeper (Click Here to See) - and I separate each little container into two. I can hold up to 32 different charms, and at least 25 of each (but could fit more). The container is easy to move, and store. Prints, prints are harder for me to store right now, so I usually only bring 10 prints of any image at a time.
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How far in advance do you order things for your table?
As early as humanly possible.

/>/>/>/> The earlier the better, and the less in expedited shipping you'll pay. Check with any online ordering to see how long it takes to receive and order. The print place I use to print my comic books takes at least 1 month for the initial printing batch. When I got my printed charms, those took at least 6 weeks from overseas at the UK to get.
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Problems you may expect to run into?
Not knowing where to check in. Staff being a little discombobulated. Try to get as much info as you can, and be as patient as you can. Sometimes things are just out of everybody's hands.
Cranky moms/dads/customers who look at your things and say "I could make that." Don't be disheartened. You'll get a few of those, just smile and be as pleasant as you can. Also include cranky parents coming up to your table with their kid and saying "You don't need any of that crap." (I have had this happen). They'll often skulker off real fast anyway, so don't even worry about em.
People trying to barter with you or haggle you down. Stick to your guns. (Unless you've some how managed to price yourself exorbitantly high.) This is your artwork, and not only are they paying for the product, but your knowledge, experience and expertise in making your product.
This is important when doing commission AT the booth. I used to have large color commissions set at $15. I would get SO MANY requests that I had to turn people away and my arm died. It also was NOT indicative of the time it took me to make one image. (I would be making like $5 an hour per image at that price). If they are confused, tell them WHY your prices are set that way: Usually due to the time and effort it takes to make your image.
People asking for off-the-wall commissions. I draw mainly lighthearted things, and I've had to turn away customers for asking me to draw obscene things that made me uncomfortable or things I just plain don't draw. Just smile and tell them why, and in my case I usually point out that I would not be able to do the picture justice.

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That's most of the big "problems" I can think of right now. I've got some funny stories of things people have asked to barter with.
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Best places to order prints, etc from? // How & where do you order your stuff/get your stuff made into merchandise? (Websites, stores, etc)
For prints, I go to my local FedEx and have them printed on bright white smooth cardstock (80# i think?). I am looking to eventually find a local print place to make even higher quality prints for me (I just haven't had the time or cash at the moment).
BUSINESS CARDS. I don't remember if anybody mentioned this yet, but BUSINESS CARDS. This is important! Have a business card with your shop name, your name, a website if you have one and possibly an email they can contact you for future commissions. Preferably with a picture of the type of artwork you do. DO NOT USE A TEMPLATE PROVIDED BY THE COMPANY. Take some time, create an image unique to you! You want people to remember who you are, and you're using the same template the guy down the row is, how could they tell you apart?
I use Print Place for my cards, and they came out beautifully!
Click Here to go to Print Place
Charms and Stickers I've gotten through Zap! Creatives:
Click here to view Zap!Creatives
And my comics I get printed by Ka-Blam! Printing:
Click to view Ka-Blam! Printing
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Average amount of art to draw? How many different pieces do you usually draw up?
Your first alley will be a slog of artwork (so stretch those hands a lot). Draw as much as possible, draw on old artworks you like and would possibly want to sell. (assuming you've saved it in a high enough resolution for printing - re-scan if needed).
Biggest suggestion? If you're drawing from a series, and you have separate images of characters, try to either hit most or all of the main characters of the show. Then you can arrange your product by series!

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Using a piece of art on more than one piece of merchandise.... how much is too much?
I would say using the exact same image on more than 3 things would be excessive. I draw little chibi characters, which I can make an 8x10 print, Cell Phone Strap Charm, Button, and/or Stickers. However, I vary each one. The print has a cute background I've added. The charm has the full body of the character, the button only shows their face. Stickers I add other shapes and multiple characters on the sheet.
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Pricing what you sell? How do you go about pricing your stuff?
You want to price your artwork to make it worth your time, the cost of supplies, and enough profit that you can make some money (and make more products from). This is where that spreadsheet with your costs on it comes in handy!
Also, I strongly suggest looking at your level of skill and compare it with other prices of people's prints in other alleys. If you are a newer artist and maybe not as honed in your skills, selling your prints (on printed thin computer paper) for $10 a pop will probably not do well. The money comes with experience, exposure, and quality level.
Don't under price yourself. Try to resist selling things like 8x10 prints for $2, or sketch commissions for a dollar (unless they're super small/super fast). Doing so not only devalues your own artwork, but creates a weird economy in the alley.
Looking back at this, it's kind of vague. I would say, look at other alleys (or try to recall them), see how their things were priced. Look at your artwork, and try to objectively say, "would I by that for X amount?". Ask others when you come up with a pricing scheme.
Like others have said: Use rounded up dollars. Things in multiples of 5's work well. People like particular numbers and $1, $3, $5, $10's work well for lower priced items.
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Tips and tricks on how to draw people to your table? (The way you set it up, merch you offer, etc)
I agree with the others on having a large, high profile item/image/etc to bring em over, and then they'll see the rest of it. My other main advice is go vertical! Whether it's interlocking cubes, wire panels, or pvc pipe, upwards is the way to go.
#1: Almost all the booths have vertical displays. If you don't have one, you'll get somewhat buried in the tables around you.
#2: More real estate to place your products!
#3: They need to see you over the heads of the other attendees.
I like to keep my main products close to eye height. I rarely have things down on the table (people hardly look down). I put my big pictures up above eye height to be seen from a distance to draw them in.
Oh, and make sure they can SEE you. People like to see the artist (usually working on something is the best way to start a conversation), and if you can see and talk to them, your are more likely to make a sale.
Have a variety of products ranging from small $1 items, to your larger things. If all you have are $50 plushies, you don't catch the people looking for a cute impulse buy for their friend.
Have deals! I sell buttons and cell charms at $3 a piece. However, I offer two for $5. People like saving money (even just a little bit) and if it's cost effective, DO IT.
DON'T have a Sunday "I don't want to take it home with me" sale. As tempting as it is, I find that I feel like I've cheated all the other people out of a good deal and it creates a mentality in the customers that they need to wait till Sunday to buy ANYTHING.
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Policies on Fanart?
Like everybody else says: Follow the rules of the convention. If you don't, you'll get shifty eyes from artists and if the staff find you breaking rules, they'll have to have words with you. (If you were unaware of a rule, just apologize and take the piece down, it's much easier than making a stink and getting banned)
I myself actually tend to follow about a 50/50 rule at my booth, as I'm finally getting into the world of webcomics and printed comics. (Trying to make a living as an artist finally!). I use the fanart to draw in the customers, (I make pokemon badge sets), and then when they're there, they find my comic and will flip through it and more often than not, I've made another sale.
I'm gonna put my extra advice in a second post, so that way it's not so long.