In order for them to obtain F-2 or J-2 status, they need their own I-20 or DS-2019. The application is available here, select "Update I-20 of DS-2019"
The I-20 or DS-2019 for your dependent will be issued in five to seven business days. If your spouse or child is still in your home country, you should mail the documents to them. They will need to apply for a dependent status visa at the nearest embassy or consulate.
Your dependent will need:
- The I-20 or DS-2019 that ISSS will issue when your application is complete
- Proof of their relationship to you (marriage or birth certificate)
- Proof of financial support (bank statement, assistantship letters, etc)
- A SEVIS fee is not required for F-2 or J-2 dependents
If your spouse/child is in the United States in a different status, they will have to file an application for a change of status. Information on how to apply for a change of status is available here.