How do you teach a 3 year old to use the toilet?

Join the club!
My son is 3 and I am having a heck of a time with him too.
he will pee on the toilet and sometimes he will poop in it too, but most of the time he runs and hides and does it in his clothes. its tough. we have been going through this for months. but eventually they will pick up on it.
they just have to be ready.
with my other kids I had them trained in their two's, but all kids are different.
just be patient with her & keep trying.

Unfortunately i think the problem is that you've left it so late to start.
I think the average age to start with potty training is from about 18 months.
My daughter isn't old enough to use the toilet yet but start with buying a potty, let her pick it out & maybe find one that praises her for doing something:)
We got our daughter a Winnie the Pooh one that has praise phrases when you flush it. It will be more her size than a normal toilet & she'll probably have more luck using it.
Start slow, if she feels like she has to go, get her to sit on HER potty & just have her stay there until she realises what she has to do to get it come out!
I am only guessing here - from what my in-laws have done with all our nieces & nephews.
I wish you well!