Here's what I paste to all people about to attend their first event:
When you and your opponent sit down, you usually say hi and shake their hand. I usually ask their name to make sure I have the right opponent. Once I almost played a guy named "Nick" when my real opponent was "Mick" Then you'll shuffle your deck thoroughly, then kinda place or "present" your deck between you two, but nearer your opponent. You then can shuffle your opponent's deck, but a simple cut is more common. Any time that you search your deck, find your cards, then shuffle your deck and present your deck to your opponent like at the beginning of the game. They'll probably shuffle or cut it.
Before you you look at your opening hand cards, ask your opponent "high roll?" then roll a dice or two. Whoever rolls the highest can choose to either "play" or "draw", meaning play first or play second and draw a card. Then deal your 7 cards, person who decided to go first will then decide to "mulligan" or "keep". Only after the second player will decide the same. If you do mulligan, you draw 1 less card than your previous hand. Okay, now the game begins. Before you go to the combat phase, say "starting combat?". These things give your opponents an opportunity to use instants or abilities or whatever before attacks are declared. When your turn is over, say "pass turn" or "go ahead" or something similar.
Other than that, just play normally. If you're the loser of the match, say good game and extend for a handshake. Don't ask your opponent about their deck (what colors are you playing?) except after the match is over. Be friendly, but "read" your opponent. If they seem to not want to chat during the match, then don't. Have a pen and paper to keep track of life, and maybe 3-4 dice to use as counters, but if you don't already have dice, don't worry about it too much.
BTW: don't get discouraged if you don't do well your first time draft. Limited is a very rewarding and dynamic format and my favorite way to play magic. Have fun and don't be afraid to call for a judge.