Comunication Problems

Chatting through steam and sharing files with dropbox would probably be the easiest and most simpliest since it's just two of you. @fubarFX might be able to help out a bit more, as he's done this more.

You don't really need live voice chats as you can't easily work same time with the map. As @Fr0Z3nR said, share map files somewhere. When using Dropbox you should zip the files because pure .vmf can get corrupted

Collaboration is difficult and there's no easy way to do it. The most common software development practice is to use version control to sync files across teams, this can work for mapping but is not exactly straight forward if you don't know what you're getting into. Sharing files on dropbox would be a straight forward possibility but has its own limitations as well (the most important one being only one person can work at a time). As far as communications go, steam is more or less crap. You'll want to be using something that has an history. One more recommendation would be to build a todo list so you guys can have an idea of what needs to be done in the project and how tasks should be divided. it will make your life easier when it comes down to knowing who's doing what and when.

A good tip is to have dev versions, for example:
User 1 starts the koth_mapmap_a1 so he names the vmf koth_mapmap_a1_dev1
User 1 sends user 2 koth_mapmap and he finishes a1, and names it koth_mapmap_a1
So this way User 1 can download the bsp and not run into naming problems.

@CriminalBunny can atest to this, but make a google doc or some method of sharing progress on the map via screenshots and a personal changelog helps.