U need to apply for H renewal, before ur current H expires. Else, u will be out if status.
u will get a new I-94 with the approved H1. If u have not got a new I-94 with the new H1 - u need to go out of US, get visa stamped and enter US.
As long as u have maintained us legal status all through ur stay in US - it wont be a problem for getting a H1 extension.
U need to send the following to ur BCIS service center.
1.Send the I-129 form and H supplement
2. I-129 W.
3. Letter fom petitioner
4. LCA copy.
5. Ur I-94 s
6. All I-797
7. recent paystubs
8. Educational qualifications
9. Filing fee
10. Copy of visa stamps