There are mainly 2 ways to go:
1. Your employer help you to apply green card. Generally, if you are hired by a company, you can follow this path. For the detail procedure, please discuss it with the Human Resources of your employer. Follow this way, you must apply LC (Labour Certify?) first, then submit the form I-140.
2. Apply green card yourself. Mainly, the post-doc in a university follow this way. There are 2 types you can apply with: EB1a (Extra-Ability) and NIW (National Interest Waivor). Roughly, the EB1a requires you have well-known results and so on, so that most applicants follow NIW. Application procedure for both EB1a and NIW are same:
Fill the form I-140, and collect necessary supporting documents. Mainly, you must ask some faculty lever person to write the recommendation letter for you, there is no clear limitation of the number of such letter, but if you can have 5 or more recommendation letters are better. You should also collect all possible supporting materials to show your experience and ability, for detail, see the instruction of Form I-140, but not limited in that list and need not collect all materials listed in I-140 instruction. It includes your Ph.D. degree diploma with transcripts, CV, your self-statement to show your abipity and experience, the copies of your published papers, the evidance that you attended the high lever academic mettings, you are member of high lever academic organization, the any news media's comments about your work, and so on.
Submit all the supporting materials together with I-140. Before, you must wait the approval of I-140, then submit Form I-485 and other necessary forms, but now you are permitted to submit I-485 before I-140 approved, or submit it together with I-140. It is hard to say whitch it better.
If you apply green card by yourself, you can submit materials yourself, or find a lawyer to do it for you, of course you must pay to the lawyer.