Beginning to exercise some control over bodily functions can be a big confidence booster and source of much pride to a small child. You want to nurture this budding independence and support your daughter's developing mastery. You also want to make the "tools of the trade" very available to her, but let her make the ultimate decisions about timing their use.
Open up the topic of toileting. One of the odd things about our grownup toilet habits is that we tend to be quiet, even secretive about our own bodily functions---we say nothing when we feel the urge to pee or poop, but go off silently, close the door, and come out again afterward. No word about how we knew it was time, how it felt to let our bodies do what they were meant to do, no delight or interest in the whole process. So you might begin by creating more openness around your own elimination process---let everyone know when you feel you have to "go," sigh with pleasure when you're done on the toilet, invite your child's company while you are there.
Let your child be the expert. Instead of knowing all about toileting, jump up and down when you have to pee, and ask your daughter what you should do. See if being the one who doesn't know what to do lets her laugh and be the expert. "Where shall I go?" then when she shows you, "What shall I do here?" Sit on the toilet with your pants on and ask, "Like this?" Let her help you figure out every little step. Any time you put a child in the expert's position, it allows her to think differently about herself, and to gather confidence.
Use Playlistening around toileting. If your child is anxious about using the toilet you can pretend that you feel the need to go to the toilet but that you are afraid to do so. This may help your child laugh and release her own stress around this issue. During this play, allow your child to insist that you use the toilet, then leap away in fear as soon as your bottom touches the seat. Say "Oh no! I touched it! Help!" as you hide behind your child. If this gets laughter going, go with it. Play around with the issue until you find the piece of it that lets your child really laugh hard. Children release a lot of stress, anxiety and confusion through laughter, which then allows them to more forward with developmental milestones.
Let her take charge of how she wants to proceed. After you've generated a good amount of talk and play about your toileting moments, you can ask your child if she wants a little potty of her own. This will help her take ownership of the learning process. If you get her a potty, let her play with it while it's clean and new. If not, you both can play at the family toilet---putting Cheerios in and flushing them down, watching the water swirl, putting paper in wadded up or flattened out...the possibilities are many.
When the time feels right, some days after you've added this kind of attention to the process and the equipment, lightly ask your daughter if she'd like to use the potty. If not, that's fine. Maybe you could make it a comfy home near one of the "big" potties in the house to keep it company. Your daughter can sit on it and pretend while the grown-ups in the house use the "big" potty.
(Some children like to begin by peeing outdoors in the garden, where it can be less intimidating than in the bathroom. Others aren't warm to this idea. But if you live in an area where it's possible to let your child run naked in the yard for several hours, that kind of play can work well with outdoor peeing to create a few positive first experiences.)
If your child seems unsure about the process, there are many good books available to help her think it through.
If fears persist, do what we call Staylistening. Listen to her feelings. Even with the stage-by-stage introduction we've described, some children carry a set of deeper fears around toileting. For these children, there's no going gently toward toilet learning. But as a parent makes intermittent attempts, they usually indicate times when their feelings of fear or upset rise to the fore at the mention of using the toilet. This isn't a time to back off. Get down, offer warmth and eye contact, and keep offering the nudge that lets them feel their upset.
For instance, if you mention that you think it might be a good time to try the potty, and your child says "No!" emphatically and stomps off, and this has happened each of the last 5 times you've offered that observation, it is time to follow her, put your arm around her, and say, "You know, I'd like us to go into the bathroom and think about peeing in the toilet." You don't have to drag her there, you don't have to do anything at all except listen to her feelings, and keep saying you'd like her to try it. After a good cry or tantrum, your child will have released some of the feelings that are in her way of considering trying the toilet. She will be open to getting closer to it than before, and might tell you what her fears or worries are. It's very important not to force action on your child's part, but to indicate what action would be good to try. She'll be letting out her feelings about the idea that scares her, without being overwhelmed by your superior power or will. Simply listen with interest and confidence ("It's safe to use the toilet, sweetie. I'll stay with you.") until she doesn't feel like crying any longer. If the fear goes deep, this could easily take up to an hour. Don't worry. It's healing to cry in your mommy or daddy's arms, to let go of the upset that keeps you from noticing that the toilet is actually a safe and interesting place.
Toileting is one of those things no parent can fully control. Your child will not leave for college in diapers. It can be hard to wait for a child to decide she is ready to use the toilet. You may find the situation frustrating and it can be very helpful to have a friend listen to the jumble of aggravation that often builds up in a parent's head during times like this. Getting your own frustration out will help you warmly remind your child that you know she can do it. Your confidence and lightheartedness are important to her now. This is a wonderful opportunity for you to reinforce how much you love and accept her as she is, regardless of which behaviors she is ready for at this moment.
I hope this helps. A more thorough explanation of Playlistening and Staylistening is available on the site below.