Get a route map. Don't only get the map, if there's a website, check it for a spectator map. Also check for road closures. If there's no website or no information, it doesn't hurt to call or e-mail the race director... just remember that they might be busy and might take awhile to get back to you, but trust me, race directors love to have spectators along their course! If you can get out there beforehand, you might scout out parking as well.
Pick a spot beforehand. Don't just go for the finish (although the finish is nice too), but runners really like seeing supportive friends and family along the course. I have spent entire races just trying to hold up until I saw the next friend at mile 6 or mile 9. Think about where the participant(s) will likely be having the hardest time. For me, a friendly a face at mile 10 of a half marathon can carry me through to the end. For a marathon, don't forget the mile 20 bonk... might be a good place for some support and motivation. If it's an out-and-back course, you can pick a spot and see your runner twice.
Show up early. Nothing is worse than getting out there and finding a crowd or a lot that's blocked off and you miss your runner. It might make for a long day, but I promise the participants will totally appreciate your presence.
Bring some flare. What do I mean... well, the more fun you are, the more excited the runners will get. You could dress up... themed costumes or matching tutu's (trust me, runners don't find tutu's weird, you'll fit right in). Maybe make a fun t-shirt... or bring some signs! If you have some specific people you're cheering for, considering making a sign specific to them on one side and then on the back, put something more generic that would apply to the rest of the participants. Consider bringing some noisemakers... cowbells are welcome! Pom-poms are welcome. Get creative, have some flare! Here are some funny sign ideas, but I'm sure there are a million more out there - I've seen tons of hilarious and motivating signs.
Cheer on ALL the Racers. The participant you're cheering for is lucky to have you there but remember that there are tons of other racers that don't have anyone there to cheer them on. There's nothing worse, as a runner, to be really in need of support and to pass a bunch of spectators who aren't really paying much attention. I know we all need a break from cheering and holding signs, but as much as possible, try to stay attentive and cheer for everyone who passes by... especially those who look like they might need a little pick-me-up.
Are there things you can hand out to runners? Perhaps. If it's a race with few water stops and on a particularly hot day... bringing bottled waters could be a blessing to many. Some spectators like to bring gummy bears or orange pieces or banana halves to offer to runners. Some cold rags soaked in ice water on a really hot day can save some runners as well.
But the bottom line... show up and cheer. Even if it's just you, barely making it on time at the finish line... any cheers and support are very much appreciated by all runners, guaranteed!!!
Runners: I'd love some additional suggestions for spectators in the comments!!!