If you are only sightseeing in China you will need a tourist visa. This visa usually covers a period of 30 days, though you may be able to get a visa for a longer period of time if you request it.
Apply for a business visa if you are attending a meeting or seminar in China. If you are studying in China for less than six months (through a language exchange or study abroad program), you will also apply for a business visa. (See below if you will be studying longer than six months.)
If you are studying in China for more than six months, you will require a student visa, which will be issued for the length of your program.
If you get a job in China, you'll be issued a Z visa. This visa allows you to work legally, and for your family to live in China while you are working there.
If you are retiring to China you should apply for a resident visa. Holders of these visas are not permitted to work in China, so when applying you will need to prove you have sufficient funds in a bank to support yourself.
To apply for a Chinese visa, you will need to fill out the appropriate forms and supply the necessary documents. To find out exactly what's needed for your type of visa, contact the Chinese Embassy in the United States.