This is Marvel comic book universe Deadpool. In the canon continuity we're loosely around Agency X era - post-Cable & Deadpool but before Evil Deadpool.

This should make things fairly unconfusing to readers who are only familiar with the movies. Salient differences in the setting will mostly be explained; the only thing that might be confusing without context is the references to the specific features of Deadpool in the comic medium. So:

1: Deadpool's speech bubbles are yellow, instead of the customary white.
2: Deadpool has 'little yellow boxes' which represent inner monologue, in the fic these are block quotes.
3: There are also sometimes white boxes which are the same sort of thing but come from a different, usually saner part of Deadpool's mind; these are block quotes in italics.
4: Arguing with his own inner monologue, sometimes out loud, is standard Deadpool.

There are some scans here which give you an idea:
http://www.dorkly.com/post/76177/deadpool-again-part-4-holy-crap/page:6