Yes you can save the seeds, but if it is a hybrid melon you will not get the same results from that seed.
If you want to try it anyhow, it is very simple to keep the seeds, just rinse seeds off and place on paper to dry. When dry store seed in cool, dry place.
Good luck

if seeds of hybrids do not grow true to type , does that mean that all hybrid melons are propogated from plant materials and that it is not possible to buy seeds of hybrid melons?

Lychee:

I am not sure what you want to know from the questions you have asked. Of course all hybrids are propagated from plant materials. What other kinds of materials could be used for propagation?

Hybrids are produced by controlled cross-pollination of selected varieties. Hybrid melon seeds are sold everywhere, and it is quite possible to buy them. I do it all the time, since I generally prefer hybrids over open-pollinated varieties. But I would never try to save seeds from them to grow out the next generation, since I would probably get results I would not like. I leave hybridization to the professionals, since I am a melon grower not a seed producer.

If you want to grow Crenshaw melons, buy some Crenshaw seed. It is widely available in many seed catalogs. Crenshaw may be an OP variety that would produce true to type, but you cannot be sure of that in a supermarket melon. I am surprised you would be considering such a thing after your recent unfortunate experience with Galia melons.

Don Yellman, Great Falls, VA

Last year's cantaloupe produced tons of melons, it was a hybrid. This year I only got one melon and it was from a volunteer from last year's. The plant produced a lot less and the melon was a slightly different shape and a little larger.

Seeds from an F1 are not likely to produce the same results as the parents. They usually revert to one or the other of the parent plants.
As you go down in generations you get more likely to have the same results as the parent.
If you had other melons in the same family odds are they crossed and you have seeds that will produce another first generation.

Sometimes the desired results of the breeders comes at F2 so some hybrids seeds are F1 and some are later generations. Since we don't know the variety or what generation it was we really can't even guess what your results would be.
You could save your seeds from your F1 hybrid, your F2 could be very different and if you saved the seeds from that your F3 could be different again.
I don't know at what point in the generations they consider a hybrid to become open pollinated.

Unless you did your own unintentional cross pollination an open pollinated plant will breed true. Many of the heirloom varieties are old seed catalog inventions and the original stories of the seeds being handed down from generation to generation were the biggest invention about them.

I prefer the flavor of open pollinated varieties for everything but corn and I like saving seeds. With melons I get more reliable results with hybrids so even though I want the flavor of OP I'd rather have melons.

If you wanted to save the seeds and still get results, plant one vine of your saved seeds next year and see how it does. If you like the results the year after only plant the seeds from your original saving.
If you just want to be a seed saver you would save yourself some years if you started out with OP varieties.

"What I am trying to understand is, if seeds taken from a hybrid melon will not grow true to type, where do the hybrid seeds we buy in a store come from?"

It depends on how the plants flower.
If they're bisexual closed flowers you may have to cut into the flower before it makes pollen, remove parts from one and put them into the other.

If they're open unisexual flowers (like many melons) it could be as simple as planting a row of each parent and removing all the male flowers from one row and all the female flowers from the other then letting the bees do their thing.

Thanks MYK- very helpful.