I know of a couple who are married he is a u.s. citizen his wife is a illegal immigrant, they recently had a child here in the u.s. what can she do to become a legal resident.

He can sponsor immigrant visa for her. Since she is illegal alien, they would need an experienced immigration attorney to file a waiver.

I have no idea how she entered US... if she entered US without inspection, she will have to return to her home country for visa interview. If she just overstayed her visa, she may not need to leave. Adjustment of status can be done here... but either one, you need an attorney.. a good one.