How do I know the nursing home is taking good care of my mother?

You visit as often as you can. Let your eyes, nose and ears provide information.
Encourage friends or family visit and inform you.
You contact the facility and if you are able to be included ask to attend Care Meetings.
You can ask mom.
(If mom has dementia take what she says with a grain of salt)
I am a firm believer that the more you are involved and the more involved you are with your mom the staff will be mo re involved with her.
If mom is eligible for Hospice the Hospice Team will keep you informed and it is another set of eyes on mom.

There should be visible signs that she's being taken care of, from clean diapers and clothes on to having teeth and hair brushed.
And if she's bedridden, that someone is coming in every couple of hours to move her in the bed so she doesn't get any bedsores.
Hopefully you or someone else is visiting her regularly and at different times of the day to make sure that she in fact is receiving the best care possible, which sadly isn't always the case in these facilities, thus why family and friends popping in randomly can certainly help ensure that she's being properly cared for.

If you are in the area, visit her. If you live far away, have a family member or friend go, or hire someone to go in to see her a couple times a week. Make sure she is clean, dressed, hair combed, teeth brushed, and has activities if she is able, etc. The nursing home should have a social worker who will talk to you every week about your mother's condition and what is being done for her.