Note: you can file application for a work permit only on or after May 26, 2015, and you must be eligible to apply.
Application form is USCIS form I-765, and the filing fee is US$380.
Note: it is applicant's burden of proof to provide evidence of your status, your H1B spouse's status and prove that you meet other eligibility requirements. Your application can be delayed or denied if it's incomplete.
Eligibility requirements: you are eligible to apply for a work permit if you are the H-4 dependent spouse of an H-1B nonimmigrant IF your H-1B nonimmigrant spouse:
- Is the principal beneficiary of an approved Form I-140, Immigrant Petition for Alien Worker; or
- Has been granted H-1B status under sections 106(a) and (b) of the AC21. The AC21 permits H-1B nonimmigrants seeking employment-based lawful permanent residence to work and remain in the United States beyond the six-year limit.
Read here.