Update 4 Sept 2010
The Melons, Cantaloup Charetais Jerac F1 which I purchased in France as small plants have done really well. I have picked 3 or 4 of each plant, they are not quite as sweet as some melons but produced good fruit and no plants rotted off as sometimes can happen.
This one I picked slightly too early, as they do turn pale yellow. Luckily it matured in the sun and was soon consumed, laced with some port.  

Follow this section as the season progresses. June 2010.  My melon plants are looking very healthy so far. I have made another video to show you how to save the side shoots to produce the melons on. The shoots are bigger so it easier to see what I do

The first two pictures are 2009 crop.
Melons are a hard crop to grow, but well worth it. They do like plenty of heat and light, but I did have some success last year. You will only get about 4 melons per plant, and you have to be patient.
The best way to grow them is to cut off any melons that form on the stem. The flowers that do not set on the stem are male flowers and you could use these to polinate the flowers on the shoots which will be female, but I have never bothered.
The plant needs to grow to the crop wire, about 6ft, then nip the head off. The fruits will be produced on the stems. Cut off the bottom 2 or 3 shoots. On the next shoot leave a fruit set, then cut off the rest, leaving at least 2 leaves. Do this with a maximum of 4 shoots.
As the fruit swells, support it in a net tied to the wire, I use tights. If one melon turns yellow too small it will not grow much more, so cut it off and start a new shoot. The plant will do this because it can only produce so much fruit per plant.
Treat the plants as you would tomatoes for feeding and care, but be careful of over watering, they are very sensitive.
My 2010 plants are coming along well, the stems of melons are quite thin, so they will soon need a small stick for support and I have just started to give them a liquid tomato feed.
A short video of my melon plant May 2010
Some people do polinate the female flowers with the male ones. I have never had to bother with this, as I never seem to get a problem with my melons polinating, but maybe thats the variety that I have grown. So here are two pictures so you can see which is male or female, notice the female flower on the right is slightly more bulbous.
So if you do want to try, here is how someone else has done it
You can pull off the male flower petals to expose the stamen, coated with pollen. I have read several very detailed instructions on how to transfer pollen from male to female flowers. Using a small art brush seems like a good idea and it certainly prevents damage to the flowers. But I tend to default to a more brute force approach.

Female watermelon flowers don't open for very long so it helps to identify them as soon as they appear and be prepared to service them as soon as they are ready. This is typically a one morning affair. When I inspect the plants in the morning and spot a female flower open, I pull off an open MALE flower. Make sure you don't pull off a female by mistake! Don't bother with flowers that look like they are about to fall off or aren't quite open yet. You need flowers that look like they are at their peak: males loaded with pollen, females fully open. With the male flower off the plant, pull off it's petals. I do this to expose the anther which should be loaded with pollen.
Hand pollination is a simple matter of uniformly transferring the pollen from the male anther to the female stigma. With the male flower prepped I carefully wipe what is left of it across the center of the female flower. I try to get pollen all over and around the stigma. Take your time, do a thorough job and do your best not to damage the female flower. If there are more than one suitable male flowers open grab them and repeat the process on the same female flower. The more the better. That female flower is going to close up tomorrow so you might as well make use of those ready males while they are around.