Yes, it's all correct. After you get married, you have to file form I-485 (Adjustment of status) / I-131 Advanced Parole (Travel documents) / I-765 Employment Authorization. It is vital that you file the form I-485 within that 90 days because the filing of it is what will keep you in legal status. The I-131 and I-765 are free when filing together with the I-485 (you just pay the fee for the I-485). I-131/I-765 will be approved 4-10 months after filing, while the I-485 could take longer and involve another interview before it can be approved and a green card can be issued to you.
Also, when they say "get married", they mean get the paperwork signed to be legally married. A long of people confused getting married with having a wedding. You do not have to have a wedding.