How do I get crisp, clean edges in the corners where two paint colors meet?
Use painters tape (blue tape, Frog tape, lots of different names and brands) to mask off the areas you don't want to paint green. 

First, paint your ceiling and 3 walls white (2 or 3 coats, however many are needed) and wait for the paint to dry. Then, apply the painters tape to those walls and ceiling as close to the 4th wall as possible. Next, and this is the most important part, go back with the white paint and "seal" the edge of the tape with a light thin coat. Failure to do this will lead to green paint bleeding under the tape, and you'll wind up with sloppy lines at the corners. Textured walls are a pain...

Once the white paint is dry, go ahead and paint with the green, using however many coats you need. Peel off the tape carefully and enjoy!

Most painters tape says to peel off within 14 days, so you could tackle this project over two weekends if needed. Also, if you seal the tape with too thick of a coat, some of that paint could come up when you peel the tape off, so don't glob it on.