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.
A short video of my melon plant May 2010Some 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.