Immigrants, people seeking a permanent residence card or "green card," and nonimmigrants, people seeking temporary entry to the U.S. for work or temporary stays can get the run around from various agencies, and if you don't get one the right way, you could face big problems. The main governing body, the USCIS, also works with people looking for asylum, naturalization as well as working with deportation matters.
Visa applications such as the H-1B are numerous and each one has special guidelines, extensions, and processes. Reading these articles and an experienced immigration lawyer can help you understand the process and what you need to do first.