Marriage-based Green Card - when and how?

I just got my Citizenship. Now I would like to apply for a Green Card
for my wife, who is on the H1 visa. We live in NJ, in case that
matters. Few questions:

1. When can I apply for her?
2. How is it done: what is the procedure, which forms, etc.?
3. How long does it usually take?
4. Her H1 visa expires in May. Does she need to extend the visa while
the application is being processed?
5. Is she eligiable for employment authorization while the application
is being processed? When and how can she apply for the EAD?

Thanks

Dmitry