Googling the name of your city + "comic con" or "anime con" or whatever is usually a good place to start! Keep an eye out when other people talk about the cons they go to, and see if those cons are close to you, then apply for the following year!
Posting about it on artist-forums, or tweeting about it, can be good. For one of the cons I frequent, they set up this little mini-board for people who missed out on getting their own table to get in touch with people who did, to arrange table-sharing.
There are plenty of printing-options for zines - I go with a local Swedish printer, but there are many online options. I was once part of an anthology that got printed via KaBlam, but that was years ago.
As for pins and other merch - I want to recomment Zap Creatives and Awesome Merchandise. They're good at what they do, deliver relatively fast, and have a wide range of options to choose from!
The short answer is "anything you want". Some people do sketchbook-zines, some people do mini-comics, some people do illustrated prose stories, I've done a bunch that were just straight up comics of various kinds, a friend of mine I know published her travelling diary, etc.
Black and white zines are cheaper to print, colour is more expensive - it all depends on what you want to do, and what you have the money for!
The main "do" with zines I can think of is to make sure that what you want to print is at least at 300 dpi solution (colour), and preferably 600 dpi for black and white stuff. You don't HAVE to go to 600 dpi for black and white for a zine, but it comes out looking a bit nicer!
As for how they're printed - a lot of printers have templates and guidelines for you. When I print mine, I assemble them into a multi-page PDF for the interior pages, and keep the covers as separate files, because that's how my printer likes them.
Anthologies are fun! I've done a bunch of them, starting back when I was in college for visual storytelling. I've been invited to some, and seen others promoted via twitter and pitched to those. There's one called Tim'rous Beastie that will be opening for pitches in December!
Print up something small and cheap - like a bookmark, or a leaflet! - and hand them out for free to con-goers. Make friends with your fellow artist-alley tablers, and try to keep in touch afterwards!
I posted a list of general advice in this other thread a while ago:
It doesn't have any printing-advice, but it does have some general how-to-survive-a-con advice - like, bring a sandwich, and wear comfortable shoes.