I have a large family and most of us play. We've started buying a box from time to time, and we host our own drafts. It is a lot of fun. If we don't have funds for a draft, we just get the required number of packs (e.g., 18 packs for six people), and pick up something for a prize (could be just about anything).
The only thing not mentioned in the first reply was removing basic lands and token cards. Foil lands stay with the pack. For Dragon's Maze, since there are no basic lands in the packs, you only remove the tokens.
What follows are some other tips from personal experience.
Until everyone gets used to drafting, I recommend that you announce when to pass. Our early drafts ended up messed up because too many packs got backed up, and some players ended up with the wrong number of cards. Pick a card, ask if everyone picked, then say "Pass." Once you guys have done a few, it will be pretty easy. As a general rule, we hold packs (don't pass them) if the receiving player already has one waiting on the table (aside from what they may be looking through at that time).
Also, another thing that can muck things up is players who keep multiple piles in front of them. Try to have them keep only one pile. Give everyone a minute or so between packs to review what they've pulled.
In our house, two of my boys are nearly inseparable, and they know the cards the other likes to play. As a general rule, they are not allowed to sit next to each other, because they will make sure they don't compete for the cards the other will want/need. We roll dice to assign seating. I announce which seat is #1, and that numbering goes clockwise. If playing with six, use a d6. Each person roles (one at a time), taking the seat they rolled. If the seat is already taken, they roll again. The last person does not need to roll.
When you get to deckbuilding, agree on an amount of time. If deckbuilding is new to any of your players, be sure to be generous in the amount of time you allow.
Also, don't forget to have plenty of basic land available.
Decide who will act as judge of any disputes. Having a smart phone or computer handy is always helpful for checking rulings on the Gatherer site.
For brackets, you can do your own on paper, or you can use a free site like Challonge.com. I like that site because it will let me have Swiss pairings (everyone gets to play every round), in addition to standard single- or double-elimination events. Here's an example of a bracket we had for a little event we did on Mother's Day (at my wife's request!).
Have fun!
P.S. I also like pack wars. Each person starts with one booster and 15 basic land (three of each color). Together, that's your deck. If you win a round, you get another pack and may add it to your deck.
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TradelistBlack and Blue--not just for bruises anymore.