There are several USCIS forms that you and your wife will need to complete and file with USCIS. I encourage you to go to the USCIS website for further information, The forms you will need are I-130, I-485, G-325A (one for each of you), and I-864 - an affidavit of support on your behalf. You will also have to provide supporting documentation such as your birth certificate, your wife's birth certificate, marriage certificate, proof of citizenship, evidence of dissolution or termination of prior marriages and passport photographs identifying each of you.
Since you are in legal status, you will need to provide proof of your legal entry and current status. I encourage you to consult with an attorney to ensure the process and all the paperwork submited is in order. USCIS website linked below.
The forms to file concurrently are: I-130 - Petition for Alien Relative, I-485 - Application to Register Permanent Residence or Adjust Status, I-131 - Application for Travel Document and I-765 - Application for Employment Authorization. Supporting forms will also need to be filed (Affidavit of Support, Biographic Information Forms).
The USCIS filing fee is $1010 for all of these forms and includes the required fingerprints/biometrics. There are photographs, supporting documentation and a medical examination by a designated civil surgeon that must be included as well as financial information on you, your wife and/or a co-sponsor that will be required depending on your financial situation.
If all goes well, you will be scheduled for fingerprints and then for an Adjustment Interview. If at the time of the interview, you will have been married less than two years and your application is granted, you will be issued Conditional Residence Status that is valid for two years. Prior to the second year anniversary, you will need to submit an application and fee to Remove the Condition from your Green Card.
Although generally considered one of the easiest paths to permanent residence, it is still advisable to at least consult a local qualified immigration lawyer if not retain one to represent you for the case. As with most immigration matters, there are pitfalls to avoid.
To chime in further - you can file Form I-765 in such a case to receive an unrestricted work permit, good throughout the pendency of your i-485. Technically this means you no longer have to work for your H-1B employer. However, if you do choose to work for someone else using your work permit, your H-1B will be invalid. This means that if something were to go wrong with your green card application, you may be left without status. If you want to work for another employer, please consult an attorney before doing so.
You can file an immediate relative petition and an adjustment of status application. In general, and as a precaution, we recommend that you maintain your H-1B status through the time you obtain your green card.
Green card holders and travel Immigration Green cards Employment-based green cards Adjustment of immigration status US visas Employment Authorization Document Immigrant status Employment Foreign and immigrant workers Form I-485 (adjustment of status) Spousal immigration Form I-130 (alien relative) Birth certificate Marriage