ADVERTISE. Create a thread in your regional zone forum, or in Tournament Discussion if you're expecting a large (50+) turnout. Make your post easy to read. Spell-check it. Make sure you use proper grammar. Don't make your audience struggle to get the information they need. Use colors and bold/italics sparingly, and only to highlight important information like addresses, start times, and special rules. Large tournaments can benefit from posting threads in regional zones asking for help with equipment and housing.
BE ON TIME. No one else will. If you open the venue at 8AM, be there by 7:30. Decide on a time to start your first event and then tell everyone to show up an hour earlier. It's the only way you'll ever start on time.
COMPUTERS ARE YOUR FRIENDS. Bring a laptop to the tournament and find a piece of software to help run it. Tournament Maker 2 is a popular choice, but there are superior alternatives. Download the software ahead of time and make sure you know how to use it. Bring speakers and a microphone if you have a soft voice. Also consider bringing a second monitor -- most laptops (and PCs with dual-head video cards) will let you mirror your display onto the monitor, so your players can view the bracket without crowding around the computer.
DON'T TAKE MONEY FROM THE POT. The only time it's OK to take money from entry fees is to pay for venue costs. The electricity cost of running one TV for 10 hours is negligible, so don't use your utility bill as an excuse to charge money. You aren't running a tournament to make money -- unless you actually are, in which case there are FAR better things you could be doing to that end -- you're running a tournament because it's FUN.
EXPLAIN THE RULES. Make sure everyone at your tournament understands the rules, from counterpicking to random stages to double blinds; having printed rule sheets available at each station is also effective. This is especially important for non-standard brackets like round robin pools. And be sure to apply the rules equally to all players. If someone gets screwed in a set because they were told a different set of rules -- especially if they were told by a staff member -- then the set needs to be replayed.
FIND HELP. Running a tournament is beyond the abilities of a single person. Ask for helpers before the event and make sure they know you'll be counting on them. Helpers can assist you in collecting entry fees, monitoring stations, preventing friendlies from taking over, running pools, announcing matches, setting up, tearing down, and reporting scores.
GIVE PLAYERS A CHANCE TO REVIEW THE BRACKET. Ask them to alert you if they play one of their friends or crewmates early in the tournament. While you're under no obligation to change such a scenario, it really isn't much work and will make them much happier. No one likes to play their friends in a tournament. Some software programs will automatically create a bracket so players from the same location don't play each other; figure out if yours does and use it if you can.
HOST SMALLER TOURNAMENTS BEFORE GOING FOR THE BIG TIME. Don't try to run a regional bonanza without throwing a smaller local tourney first. You'll learn more than this thread could ever teach you and people will learn to respect your name as a tournament host. Respected hosts get the big turnouts and the hot chicks (it's true).
INTRODUCE YOURSELF. Make sure everyone knows your name and what you look like; the best time to do this is when taking signups. Ask the name of everyone you don't know and tell them yours in return. It's as good a first impression as any, and someone who likes you off the bat will be much more forgiving when you yell at them to stop playing friendlies later on.
JOKE AROUND. Try not to be completely serious all the time. You're running a video game tournament, so have some fun. This will also make people like you more.