How do I get my Alzheimer's mom to eat?

You did not say what stage of her disease she is in. If she is in the early or moderate stage, have her evaluated for depression. Often people don't eat when they are depressed so you want to rule that out. Also their are medications to stimulate the appetite.
Make sure you know what she wants to eat. It may not be the healthiest food but might get her eating again. My grandmother ate ice cream for the last year of her life and lived to be 103!

Talk about food before the meal and then see if she can exercise a bit which may help her to feel like eating.

If she is in the advanced stage of her disease, she will eventually stop wanting to eat or drink. It's just the natural process of the body shutting down. It is not painful to stop eating or drinking at the end of life. You can keep her lips moisturized and offer ice cream, puddings, lollipops, also I use sections of oranges that in the advanced stage of dementia people seem to still enjoy. I think the scent of orange is stimulating and they may like to suck on the section or the orange.

If your mother is in the last stage of her illness, you may just be able to comfort her with your presence and loving touch.

I hope this is helpful to you.