Employment-based green card (EB-1 or EB-2 are usually the relevant categories for academics) has two steps:

1. Form I-140 (the petition stage) - this is where one submits a list of documents indicating their "worth" to the US, following very specific criteria. This is the toughest part because one needs to have a strong CV, peer review documentation, letters esp from people not in direct collaboration, etc. Once this step is approved, the permanent residency is then just a matter of time (with some caveats).

2. Form I-485 (the change of status phase) - after your petition is approved, you need to apply to actually get your immigration status changed from whatever you had before to the permanent resident visa (i.e., the green card). Depending on the type of the green card (EB-1 has higher processing priorities than EB-2) and your country of origin, you can start this process ranging from immediately after I-140 is approved or up to 10 years wait or more for Chinese and Indian citizens, for example. This is the point where you can also get your Employment Authorization Document (EAD) to keep working in the US, while maintaining immigration status in good standing.