How do I apply for an Employment Authorization Document and who qualifies?

Good question.

The first part of your question is easy to answer. In most cases, you apply for a work permit, technically known as an Employment Authorization Document (EAD) by filing Form I-765. To be sure, some non-immigrant visas include the legal authorization to accept employment in the U.S. so no separate EAD is needed. Some common examples of this are the H1B visa, TN visa, and L1 visa.

EADs are typically issued to people who are in the process of applying for an immigrant visa that has not yet been issued. For example, applicant's for adjustment of status are entitled to apply for an EAD. Also, F1 students can apply for an EAD to pursue Optional Practical Training or OPT. These are just some examples. The instructions for the I-765 contains a complete list of those people who may qualify for an EAD.