I have written a script, but I do not know much about cineomatography. In your opinion, what is the best way for me to go about shooting a short so that it looks the same way that Days of Being Wild directed by Wong Kar Wai looked? It was shot by the great Christopher Doyle and you can view some stills here

http://www.kino.com/daysofbeingwild/stills.html

I do not know if it was shot in 16mm or 35mm. There seem to be several green/blue tints used. It is a great art film.

My script takes place inside a similar apartment building.

They light with lots and lots of gels.

They light with lots and lots of gels.

What are gels?

What are gels?You're probably going to have to do a lot of research on that. Here are some links that might be helpful:

http://www.dvinfo.net/articles/lighting/spears1.php
http://dvinfo.net/articles/lighting/spears2.php
http://www.scottspears.net/filmmakpg3.html
http://www.dv.com/columns/columns_item.jhtml?articleId=175801670

It's going to take a lot of practice and trial and error to teach yourself to get that Christopher Doyle look. I've been practicing with lighting for a while now, and I'm not even close.