Yes, they do, at 6pm.
Usually it's booster draft, but the last Friday of every month is standard.
For booster draft, you sign up at the counter at Tactics and pay $15 (best chance is doing it before friday, as it tends to fill up). Drafting's pretty easy once you get the hang of it. Basically, you sit down at a table (usually of 8 people) and get given three booster packets (15 cards in each). You open one packet, choose one card to use in your deck, then pass the rest of packet to the person on your left (you'll get given the rest of the packet from the person to your right). Again, you choose one card, and pass the rest to the person on your left. This keeps going 'til all the cards are taken. You'll then open the next packet, and same story, with the one exception that you're now passing to your right. Then third packet, and back to your left. After all this, you'll have a pile of cards with which to make your deck (minimum 40 card deck for a draft). They supply basic lands for you to use
Booster drafts are also a good way to get more cards, as you keep them after.
As for learning to play, from watching the video's you should have the general gist of it. Also, in the starter decks they give you instructions on how to play. There are also usually people playing games before drafts, and sometimes just during the day at Tactics
In any case, the people drafting at Tactics are usually pretty good, and shouldn't mind answering if you have any questions during a game.