My brother is a U.S. and he married a woman that's an illegal citizen (from mexico), I was wondering does that make a her a U.S. citizen? Because she says that she is not a citizen so she can't get a job. If anyone knows anything please give me info because I believe she is just lazy.

Getting married to US citizen alone does not make her a US citizen. Your brother needs to file a petition to adjust her status or simply known as green card, then she will be eligible to obtain SSN and driver's license.

If she does not have these 3 items, finding a job would be very difficult especially in some states such as AZ or CA where employers are required to run a background check and verify legal status before hiring. If she doesn't have any connection, the chance to get a job is very slim.

If they were married but her husband failed to file petition to adjust status for her, she's still illegal.

No it does not make her a citizen, it makes her still illegal and she can still be sent back to her nation. Also she may still have to return to her nation to apply for a legal visa to return to the US, I would hire a immigration attorney to file things for the best result for them.