Generally what happens is that you take your green card and passport, which is considered a valid indicator of your identity, to a Social Security office and you will be issued a Social Security card.
You then take your passport, your Social Security card and your green card to the DMV, and you are able to get a driver’s license or state ID. Certain H-4 spouses are now eligible to get authorization for employment documents, as are spouses of E and L nonimmigrants.
People with EAD’s (Employment Authorization Documents), such as those who have filed for adjustment of status, undergo a similar process: they are allowed to take the EAD and their passport to Social Security, get a Social Security number, then take the Social Security card, the EAD, and the passport to DMV, and they can get a driver’s license or state ID.
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