I brush my cats' teeth daily, and I can tell you, it took a loooooong
time!! It takes patience and persistence, getting the cat used to you fooling around in her mouth. But make it a pleasant experience for her, with lots of scratching and petting and praise, and eventually she might even come to enjoy it!!
Here's a good way to open her mouth: if you're right handed, hold her in your lap. Hold her head with your left hand. Position your left thumb at the corner of her mouth. With your right hand, stick the fingernail of one finger in between her lips and pry open her mouth between her incisors. Meanwhile, with your left thumb, press the lips at the corner of the mouth in between the upper and lower teeth. The cat won't bite down on its own lips.
If she squirms too much to let you do this, you might have to wrap her in a towel.
Good luck, and bright pearly whites for your kitty!!