Potty Training is a commitment. A few things that worked for us...
In the beginning, make regular trips to the potty. This is the commitment part. You have to do it regularly for it to become a habit. Go upon waking up, within 10 minutes of having any drink as well as following meals, before and after nap time, before bed time, etc. Try to figure out regular intervals that work for your schedule. Also watch for the pee-pee dance.
DON'T ASK! Just take them and say, "It's time to go to the potty!" Don't act like it is a chore. Be pleasant and patient. Don't make a big fuss over it but do be persistent and insistent, you are the adult, you make the rules....be firm and resolute. Whether they say they have to go or not is irrelavant at this point. Also, it doesn't matter if they go or not what matters is establishing the behavior of going to the potty regularly.
Give praise for success, "Isn't that better than having messy pants?" Always be encouraging, "That's okay, maybe you'll get it next time." And make sure there is a next time. Don't give up, consistency is the key here.
Make them clean up the mess, especially if you believe it was not an accident. This may mean you have to literally hold their hands and help them clean it up but I guarantee after a few cleaning episodes they will think twice about making another mess.
Once they are going potty regularly you can ease up on the "scheduled" intervals. Just be mindful of how much they drink, when the last time they went to the potty was and when the next opportunity to go will be, you should at this point be able to use your judgement. And you still need to watch for the pee-pee dance, shifting from foot to foot, and general twitchieness. Don't start asking them if they need to go until they can reliably tell you that they need to go potty. If you need them to go (say before leaving the house) then they need to go, or at least try, regardless of what they say.
Once they become experienced potty users....
You still need to make them go at certain times to avoid recreational potty trips. On several occasions my 4 year old son has "needed" to go potty, not because he needed to but because he was bored or didn't want to eat his meal. So, I still insist my children go before and after sleeping, before and after meals, and before and after leaving the house. That way I know and can say, "You just went such and such a time ago, eat your food or wailt until I'm done and I (or somebody) will take you, etc."
Potty training is one of the most difficult things I have ever done. The rate of your success is determined by your level of commitment. Stay with it and I promise, as a mother of 3, you will be rewarded!
Your next challenge is but-wiping!!!!