make an excel chart. that's what i did. i also had pay stubs so i was able to approximate how many hours i got paid for assisting in addition to volunteering
Can't answer your question about Dental schools and AADSAS, but as far as how I keep track of mine, after every volunteering/shadowing experience, I make note of it in a Word Document the day of and type a couple of details about the experience.
I don't think the dental schools verify the amount of hours you put in... that would be ridiculous if they had to do that for every applicant (or even those they interview). I think it's a thing of trust. They trust that you're an ethical person.
As for me, the places I volunteer/shadow at actually keep track of my hours for me. At two places, at the end of the day, I write in what time I came in, when I go out, and how many hours I have done for the day. At another place, they electronically keep track of my hours because they sign me in and off through the computer. But if they didn't, I'd probably just make a list and tape it to my wall and make notes of when I volunteered/shadowed. (I like the idea of writing down notable things that happened that day because that could be useful later).