when applying for a Chinese visa, do i mail my passport with the application and fee.

You cannot mail the application to the embassy of PRC to apply for it. You need to submit the application in person or entrust someone to do it for you. And both your passport and copy of its data page are needed to be submitted.

How do I get a visa to visit China?

If you go to China for sightseeing purpose, and have an US passport, the first step is to prepare all the required documents including passport and its copy, a completed application form attached with a passport-style photo, transportation arrangement, round air tickets. Next step is to submit the application to the embassy of China.