What to put here is, I think, pretty self-explanatory. Put what platforms you prefer to write over. Are we talking email only, Google Docs, Skype, forums, Facebook, Tumblr, LiveJournal, Kik, etc.? The list of possibilities goes on and on.
Now, my personal suggestion is to put one main form of contact (ie, an email) and then letting your potential partner contact you from there. You can flesh out where you really want to write via that, but I wouldn't suggest posting all of your screen names here for everyone to see. It's the internet, there's some creeps out here, okay?
Put in a line that says "drop me an email for my screen name" or "email me what you're interested in and what medium you're looking to write over." If you only have one point of contact, you can save yourself a lot of headaches.
While it's not necessary, I have seen a lot of people that will have a short "form" for potential partners to fill out when they contact them. Something so that you have an idea of what you're getting yourself into. It doesn't have to be a "form," per say, but letting your potential writing partner have a starting point for what to send you in your first message could be helpful.
Perhaps you want to know their name, their age (remember how important I said this was on the rules page?), their limitations, what genre they're interested in, and if they have any plots or ideas that they're looking to have fulfilled. To each their own, and that part is totally up to you on whether or not you want to have something for them to email you or not.