So far, the closest experience I have is being white and understanding Chinese - but it doesn't hurt nearly as much, the worst people regularly think about me is that I am an unreliable, eternal frat boy.
This is a similar story: http://abcnews.go.com/Health/cross-closet-straight-christian...
The whole masquerade part also isn't strictly necessary, putting yourself close to the issues at hand is also helpful. I've never been homeless, but I've worked at three separate organizations related to homelessness (an employment/retraining program, a transitional home, and a straight-up shelter) and met many people that way. I will likely never gain a complete understanding of what it is like, but hopefully I've picked up enough of the big things that I'm being less of a net-negative on the world.
Mark Twain once said (or perhaps according to the Internet Mark Twain once said): "Travel is fatal to prejudice, bigotry, and narrow-mindedness." - purposefully exposing yourself to different types of people along all arbitrary lines of division in a substantial way may be the next best thing.
http://www.sikhnet.com/pages/tyingturbans
or a Muslim one:
http://www.youtube.com/watch?v=9r1_HfOMRBM
I'm sure you could go to a local gurdwara or mosque and ask for pointers. They'd probably be over the moon.
It's also not particularly hard to look verging-on-homeless poor.
If you really want to do skin tones, you'll need decent makeup. If you're in a big city, just go by a serious makeup store. (In San Francisco, Kryolan is great.) Otherwise, call up your local community theater and ask them to put you in touch with a makeup artist.