J.C.
The way that I potty trained both my children was to let them run naked and I used the big toilet, they just wanted to play on the little toilet. My son actually was naked (I had taken his diaper off to change it) and he just went and climbed up on the toilet (our toilet) and stood up (yes, he stood on the toilet seat) and peed! He was 17 months old! My daughter was 15 1/2 months old the first time she used the toilet. They both were about 18-22 months old before they didn't have accidents on long car drives or before I would take them in public without the diaper.
I think the key is just relaxing and not stressing over it. Don't make a big deal about it, when they peed or pooped on the toilet we would clap and I would sing "Just went pee-pee on the potty" and that was it. I never did anything else. Ofcouse with my daughter I let her be naked, but I put her on the toilet almost every hour and let her sit for about 5 min. looking at a book and then I would let her down. Sometimes she would go and other times she wouldn't. My son, I would catch (or hear the stream coming out) and I would yell for him to stop and going on the toilet...amazingly he would stop, I would scoop him up and put him on the toilet (he is now 26 months old and still squats, doesn't like to sit and use the toilet). Eventually he began to understand the sensation and would make it to the toilet. There were accidents, but for me it was not that big of a deal. They do a great job, and it really is nice to know that they were out of diapers at a young age, considering the cost of diapers is crazy and I have a 3, 2 and 10 month old! LOL...My daughter still wears her diaper at night (only at bedtime, not nap), but my son wears a diaper at night and nap. Just a note, I used to tell me son to push it all out, you'd be amazed at how much is still left in the little man. Also some children will get completely out of the diaper, for bedtime, nap, and day....others can do one or the other, just relax and follow his que. If there is an accident just tell him that it was an accident, you're not mad, but he needs to go on the toilet. And another note, always good to keep diapers around even if the child is completely potty trained because when they get sick and have the runs, it is not fun if you don't have a diaper! That is something that takes time for them to understand that feeling.
Good luck. I know a lot of people have trouble with potty training, and knock on wood I haven't yet....but again I didn't stress over it ever, I let them tell me when they were ready and I was prepared for cleaning up messes!