I'm kinda an expert on this, so...
Naps - some people say that their preschool child doesn't need a nap. Even if the child sleeps 13 hours at night my answer is they do still need a nap up until they are in kindergarten. A nap is about recharging the body, restoring the peace in the mind and relaxing. I have found this analogy the best to illustrate my point - Cars should have oil changes about every 3000 miles. Sometimes life gets busy and we forget to do the oil change, perhaps for a while. Your car doesn't show any damage. You might even get to 6000 miles and no oil change and still the car is running just fine. But sooner or later that car is going to die. The engine is going to seize up and revolt and you will have an unhappy car. The car will not work any more. Naps are the oil changes in a child's life. They are needed even if you can't see the affects of skipping them right away.
Overtired Children - When a child is overtired they don't act sleepy, instead they get hyper. For a baby they will get VERY crabby and cry. Each child has a "window" of time when they will easily fall asleep. If you miss the signs and miss that window of time you are going to have a very difficult time getting the child to calm down. Often if a parent has a hard time getting a child to sleep the key is to make bedtime EARLIER so they don't miss that window.
Older Children - First you have to have the right environment - a DARK room, music on continuous play, sometimes a fan is needed in addition to the music, no distractions, naps not being optional, and a consistent schedule. To create a dark room I put the scratchy part of velcro on the window frame then I take black felt and have it cut so it is 12 inches wider and taller then the window opening. Double the felt up so even on the sunniest day the room is dark. (The reason for this is because our body needs darkness in order to reach deep sleep.) Other things to do -- dim electronics (I cut pieces of window cling car shades and put it over the display), remove TVs from bedrooms (A new report from July 2011 states that preschoolers who watch TV in their room took a longer time falling asleep and woke up more drowsy in the morning. Additionally, children who spent only 30 minutes of screen time viewing before bed were 28% more likely to have sleep difficulties compared to 19% who had no screen time. ) , and most of all, set an early bedtime. Most children have a built in alarm clock so I believe a 7 pm bedtime is needed to make sure they get enough sleep. This makes sure you don't miss the window of sleep and that the child will get the 12 hours a night they need.
If all that still fails, try eliminating milk from their diet. There was a study done in 2001 that showed that the majority of preschool sleep problems were a hidden milk allergy. For my experience with this, read my story below.
I have had some failure in the sleep department as a mom. I thought that it was SO easy. After all when I had worked in daycare centers I just patted backs, kids slept and nap time lasted 2 hours every single day. When I babysat I put the kids in their beds after reading them a story, and told them to sleep and they did. Maybe once or twice I had to lie next to a kid for a few minutes, or pat a back, but overall - super easy.
Then I had Tara. She was sick from 2 weeks old until 10 months old. Almost the whole time. Hard to get a kid to sleep through the night when they are coughing from RSV. Then she was failure to gain weight. She literally lost weight if she went 8 hours without drinking/eating. So we had doctor's orders to feed her if she woke up. By the time she was two I was ready to force the issue, her weight had steadied and I was ready. But the habit was there. She went to sleep great but would wake 2 to 20 times a night. Most nights much closer to 20. Right before she turned 3 we sold out townhouse but our house in Plainfield wasn't built yet so we lived like nomads for three months. Hard to ask her to sleep through the night when we were never in the same house for more then a few weeks. Then Elise was born..
See how the years of bad sleep happen? It snowballs, and becomes habit. By the time she was 3 1/2 I was at my wit's end. I could not survive much longer with two kids not sleeping through the night. So, I started researching sleep. The solution for Elise was solving her colic with a chiropractor visit and two nights of sleeping in the farthest corner of the house from her so I didn't hear her crying. For Tara it ended up that she had a hidden milk allergy. There had been a study done in 2001 that showed that the majority of preschool sleep problems are really hidden milk allergies. I took milk out of her diet two weeks before she turned 4. By the end of the first week she started sleeping through the night. Six solid nights of 13 hour sleeps had me wondering if it were just a fluke. So I overloaded her with milk products that sixth day - cheese, yogurt, milk, ice cream was her diet. She was up six times that night. Took all the milk things away again and we had a great night time sleeper. We found that two glasses of milk or milk after noon caused night time waking and we finally had solid nights of sleep for everyone in the house.