I have to disagree with those that are saying wait--18 months is a perfect window for starting. My DD is 20 months and 90% grad. She is clear on when she needs to use the potty, but we have misses in the early mornings when I'm in bed and she can't get her "just in case" pants off :-/ We rarely have misses when out of the house and only only at home when she's ill. Granted DD was first introduced to the potty at 2 weeks and was consistently using it by 6 months, but I know many people who start at or around the 1 and 1/2 year mark. In fact, in most parts of the world, babies who are not already proficient with self-toileting, start potty training the summer of their 2nd year (ie the summer following their 1st birthday), because it's warm enough for them to play outside in minimal clothing and if they soil themselves there's not a huge mess to clean up ;-).
As a PP suggested--strip her down and let her run around naked--she'll be able to connect her eliminations and feelings and you'll start to get a feel for her elimination patterns. Keep a log of "pee times" and once you get a feel for how long she goes between pees, start using a clock/timer.
Put a potty in a visible place--if she signals she needs to use it you can go to the bathroom, but the potty will be a visual reminder for her. Communicate about her feelings when she's peeing & pooping. Keep things positive, if you start getting stressed, do some minimal waterproofing (training pants are good) for furniture protection, but no so much that you don't realize that she's wet.
Great times to make a "catch" in the potty are after naps, before bed, 15-20 minutes after meals and whenever you go (toddlers love to imitate their parents). Choose some times and be consistent. If your daughter starts to signal that she needs to use the potty--take her. Keep a couple of books or toys at the potty and let her play with them while she's there.
Don't fall into the "oh you're wearing a diaper, so it's ok to pee in your pants" trap. This just causes confusion for LOs. If you are in a situation where it's impossible to take your LO to the potty, explain to her that you will take her in X minutes when Y is done and if she can't wait that you understand and will help her get dry as soon as possible. (Here's a real life example from last year: "R the plane is taking off now and we can't get out of our seats. Take off will be about 20 minutes. When the red light goes off then we can use the toilet or get out of your wet pants. Don't worry if you have an accident. Mommy will help you get dry as soon as it's safe to take off our seat belts.")
If you'd like more ideas on a gentle, natural approach to early toilet introduction, look into "elimination communication" For more information see:
http://tribalbaby.org/ECindex.html
http://diaperfreebaby.org/
http://www.white-boucke.com/reviews/latestarters.html