As noted, the actual draft kicks off at 7pm ET Monday night, but you don't have to wait until 7 for video coverage. MLB.com is running a draft preview show right now, and MLB Network will have a preview beginning at 6pm.
MLB Network will then televise the draft, live, at 7. There will be five minutes between each pick in the first round, spanning 32 selections. Once the compensatory round begins, there will be one minute between each pick, through pick 50. Day one will only include the first and compensatory rounds. Rounds 2-50 will take place on Tuesday and Wednesday, and will be broadcast exclusively on MLB.com.
We, of course, are part of a giant network of blogs, and all of the baseball sites will have coverage of the draft. I can't link all of them, but I can link Minor League Ball and MLB Bonus Baby - sites that specialize in general draft coverage, rather than going at it from the perspective of fans of a team. You'll want to follow along with them for analysis, commentary, speculation, and whatnot. MLB Bonus Baby's Andy Seiler also wrote this piece on the draft's top ten prospects, to bring you up to speed.
And Keith Law mocks the first round at ESPN, although his list is Insider-only.