An example from here in Tennessee. There are a bunch of things I don't understand for certain, I tried to make that clear.
You still have to register to vote ahead of time. I believe, but couldn't verify for certain, that anyone who will be at least 18 years old on Nov. 4 (the date of the general election) is allowed to vote in the primaries, even if they're only 17 currently.
You go to your neighborhood polling location and show your voter ID card. You tell them if you want to vote as Democrat or Republican (whereas in some states, you have to make this decision when you register to vote, and send in a form changing it ahead of time if you change parties).
You sign next to your name in the pre-printed voter registration rolls for that polling place. Then you get in line. While in line, you can look at the big poster explaining what Democrats and Republicans will see on their screens, including complete candidate lists.
When you get up to the voting machine, there's a poll worker who sets the machine to either Democrat or Republican. In Tennessee, if it's Democrat, you just vote for one presidential candidate (though there are only 2 still in the race, there were 9 or 10 democrat names listed, because that's determined months earlier). If it's Republican, you choose one presidential candidate (again, from about a dozen republican names even though only 4 were officially still in the race), but you also are supposed to choose up to 12 Delegates from a list of about 100 or so, I think. Each Delegate candidate name shows what presidential candidate they're committed to support, although a handful said they were uncommitted.
We have touch-screens. You touch the screen next to the candidate(s) you choose, and have to touch three separate "Yes, I'm really done" on-screen buttons to finalize your vote. There seems to be no paper record at all. I have no idea how they do re-counts.
Democrat delegates are apparently selected at some separate event, rather than voted on during the primaries.
Once the votes are tallied, they determine how many delegates each candidate receives. In Tennessee, both parties split up the delegates among the winners, but I believe it's more by precincts won rather than an absolute division based on the state-wide popular vote totals.
And I'll be honest, I don't understand anything about how they actually assign Delegates. I do know that when the National Conventions are held for each party, the chosen delegates will go and cast votes, then re-vote as many times as necessary until a single candidate wins. Delegates are supposedly required to vote in the first round for the specific candidate to which they were committed (as in, if I were sent to the convention as a delegate for Jimmy-Joe-Bob, I'd have to cast my first vote for him). In subsequent rounds, delegates are allowed to move their vote however they want to.
I'd imagine there's a lot of back-room negotiations followed by candidates who drop out asking their delegates to support a specific other candidate instead. For example, while Romney has now suspended his campaign, he is keeping his delegates, and will be able to negotiate a deal with some other candidate in exchange for asking his delegates to support that other candidate.
I don't know if people who dropped out of the race earlier (like John Edwards), rather than "suspending" their campaigns, retain their delegates, or if theirs are automatically re-apportioned.
(edited to mention touch-screens)
