As part of your marriage green card application you may apply for a work permit with USCIS Form I-765 (“Application for Employment Authorization”).
You normally file this form along with your marriage green card application (Form I-485) or at any time after you’ve gotten a notice that USCIS has received your green card application.
If you apply for a work permit in the same package with your green card application, you simply need to include a completed Form I-765 and two passport-sized photos.
There is no fee for filing a work permit application if it is included in the same package as your green card application.
It currently takes about 150–210 days (5–7 months) for USCIS to process work permit applications.