If your mom's financial situation is not complicated, and there's been no gifting of money or transferring of her assets to anyone within your state's look-back period, then just download the form on your county's website. You need to provide her basic info, like DOB, SS, banking info (will need "proofs" like copies of her recent bank statements, list anything like a house or car, etc. It's not rocket science. Just remember that as soon as she signs, dates and mails the form, it should take about 3 months to know if gets approved. Also, the form will ask for any unpaid medical bills received in the last 3 months to filling out the app, which they will take into consideration. Don't let the length of the form unnerve you. Like I said, if she has few and simple assets, it's not hard. Sometimes Medicaid writes back and asks for more "proofs" so make sure you open all of their letters immediately and look for deadlines, as you will only have about 1 week to send what they're asking for.
I made an appointment with our County Social Service office. The Medicaid caseworker sat with me and explained everything I would need. He actually filled in the paperwork. I like talking face to face.
That will tell you how to start an application.