One person gets here (alone or family) and files for immigration papers for their immediate relatives, starts working here (usually at an establishment of a relative or a person from the same community), makes enough money, transitions to setting up a new business and the someone else takes their place at the previous establishment. That's how the motels and 7/11,Dunkin etc. chains are run ..
This book had a nice description of this phenomenon. http://www.amazon.com/Dhandho-Investor-Value-Method-Returns/...
The FOB immigrants owning stores in Chinatown have either relations to U.S citizens (e.g., uncle, cousins) or they were born in the country and never bothered to try to learn English well (which is fine by me, since I speak Chinese as well).
Also there are quite few bars in Chinatown; they are just in the basement of the restaurants where illegal gambling takes place.
A lot of those come via green card lottery. That still means it's hard.
How do all the Chinese/Korean/Indian people in the US do it?
I often read on Hacker News about how difficult it is to start a software company in the US. But then I live in Brooklyn and people who don't speak english are always starting laundromats, bodegas, fruit stands, hardware shops, restaurants, and so forth. 3 out of the 4 businesses on my block were started by FOB immigrants. The only one that wasn't is a bar.