What steps do we need to take to get my aunt in a nursing home?

Call admissions at a few nursing homes, take tours and ask lots of questions, they will know all the steps you will need to take. The department of aging in your area could be some help also and let you see what options are available.

Gonzo, As mentioned previously, scout around your area to see what homes are there and you can usually get their room fill rate on line to see if they could "Intake" your aunt. Perhaps the biggest concern here is her money. If she is Medicaid eligible, the state will most likely take care of her. If she has a good sum of monies, she will need to spend it down to a level of qualification for Medicaid. If you are in a city with any size, find your local "Senior Services Center" and drop in and start asking questions.
Leaving her with your dad is a recipe for stress and pain for all, so do get out and look around, find a resource center and start gathering facts. The longer you wait, the sooner a crisis will arise and then all h*ll will break loose. You will quickly see that nobody will "Come to your rescue" you have to make things happen, sorry, but that is the way it is. Chin up.

Go on some nursing home tours. They are very helpful.