It does rather depend on where in the world you are. Head to the cycling heartlands of Italy, Spain, Belgium & France, and increasingly Germany & Austria, and you can guarantee that any bike race that goes through a town will be greeted with encouragement of some description. Local kids, crudely painted (and sometimes crudely designed!) banners, food, water, and if you're very lucky maybe even an oompah band. Go to the hinterlands of the UK, or northern Europe where bikes are primarily a means of transport and not a vocation, and you may very well only be welcomed by local vagrants asking "how much is your bike worth, mate?". With this in mind, I thought I'd write a handy guide for would-be spectators.
How to pick your spot.
Bike races are best watched on TV - I'm afraid this is empirical fact; if you want to know what is going on in a race, you're much better off huddling up on the sofa with a cup of tea than you are braving the sun or rain to watch by the side of the route. However, what you miss by your frankly shocking lack of committment is the experience of a passing race. For a big road race, it will start with a publicity caravan, more free crap than you can shake a stick at, a series of rolling adverts on wheels, and then finally a series of police cars and motorbike outriders before finally you catch a brief glimpse of the patchwork quilt of multicoloured jerseys before the race is gone, out of sight like a multicoloured rumbling, rattling cloud. If you want to see the riders for the maximum possible time, pick somewhere where the course goes steeply uphill, especially in a multi-lap race, as this will give you a great vantage to watch the race develop. Failing that, try to find some friendly locals who own a vineyard/brewery... Oh, and don't forget a waterproof!
How to encourage riders
Never, never, NEVER utter the dreaded words "dig in". Say what you like, give riders time gaps to the next person on the course, tell them they look good, or smooth, or fast. Offer them handy hints of how you think they can make up time or places. Make them laugh and smile; most bike riders are pretty humble and have a good sense of fun, even when racing. But just saying "dig in" is the lazy spectator's cover-all. I have often wondered, what does it even mean? What am i supposed to be digging into? My suitcase of courage? Please...! A few wise words, or a good juicy pun chalked on the road shows that you care!
How not to encourage riders
You're standing by the side of a climb. A bunch of totally knackered riders are pushing the pedals as hard as they can to ride past at a decent lick. For some reason, especially if you're Spanish, the thought occurs "I know, i'll run alongside them". Just don't even think about it! For one thing, you should be holding a glass of wine, and spilling it would be a sin. Secondly, if you can run easily alongside, it's going to be utterly crushing for the poor sods who're trying as hard as they can, and if you can't you could lose your footing and end up with tyre marks in your face... Some people like to have water poured on them when it's really hot, others not so much, so don't forget to ask. As an aside, probably one of the most pleasant experiences of my cycling life was being soaked by an Italian Nonna somewhere in the Dolomites in 42o heat, when i thought spontaneous combustion was imminent. I did get sunburn because it washed off the suncream though!
Finally, don't push people, it doesn't really help, and it can get us disqualified! Keep it dignified, and there'll be no need for anyone to get Hinault on your ass...
What you can hope to get out of it
If you're watching a road race, you'll see the whole thing pass in about 20 seconds flat, from the lead car to the last guy on the road, unless you're in the Alps and on the last climb of the day. If you choose to watch an MTB marathon race, where there are pros and punters like me racing, you could be there for more than an hour cheering for the first guy and the lanterne rouge. Either way, the main reason for going to spectate isn't really to find out how the race unfolds, you're better off in front of a TV set for that. You should expect to meet a bunch of like-minded people who're fun to hang out with, have a nice picnic, and generally soak up the atmosphere. You might get the odd freebie from the race caravan, you may just get a plastic bag to shelter you from the rain, but you'll end up with good memories of a day in the hills, and stories to tell of the epic ride you saw. And maybe even a glass of vin rouge to dull the ache of making your cyclist legs walk...