Look, baby, you're own potty!

So we bought Sydney her own potty tonight. Honestly, I was hoping I'd have a few more months until any kind of potty-training would have to commence, but I was shown, in very specific terms, that the diapers are just not that great anymore. Today is the third ... yes, third ... day in a row in which Sydney removed her clothes and her diaper, and proceeded to sit somewhere and take a big, huge pee. Yesterday's pee was on her red chair in the living room. This afternoon's pee was on my bedroom carpet. Also, she removed her diaper, and then put her pants back on, at some point during naptime, and, of course, peed in two spots in the crib. OKAY, CHILD! I am remarkably aware that you are unhappy with diapers all of a sudden! So, off we went to Babies 'R Us to purchase a baby potty. We got a nifty 3-in-1 stage potty that begins as a sitting-on potty, then can be taken apart to be a potty seat for an adult toilet and a stool. This sounds like a good idea.
After the initial freak-out argument about her wanting the potty in the living room and Mommy insisting that it belongs in the bathroom, and Mommy winning, she proceeded to sit on it a couple times (still dressed), and then hop up a couple times. We praised her every time she sat down, and then, again, explained what the potty was for. Tonight wasn't going to be much though, we knew, because it was late for bedtime for her, and she was super tired. Tomorrow is another day.
To be completely frank with you, I was not at all ready for this. I'm freaking out, actually. I was hoping to have gotten through this move, and next month's travel plans, before dealing with this in any way. But, as Brian reminded me, "She works on her own schedule." Of course, she has been showing me that for the last 28 months. I know that! What I don't know, is how on earth to potty-train a child.