Quick note on seed saving: The kinds of seeds you plant to save seeds from matters a lot. Check out this link for information.
Saving seeds for squash is basically the same for all different kinds, including pumpkins. All you have to do is pull the seeds out of the squash before you eat them. Don’t cook the squash first because it will kill the seeds. The squash should be nice and ripe before you pick them as well. The best way to be sure that the seeds themselves are nice and ripe for saving, leave the squash to grow on the vine a little longer than you normally would for eating. You can still eat the squash, it just may taste a little different than the ones you pick nice and small.
Once you remove the seeds from the squash, get rid of all the squash pulp attached to the seeds.
I put the seeds into a colander and rinsed them off really well. If there is a lot of pulp, you can soak the seeds overnight first. The smaller seeds and the flat seeds aren’t the ones to save. You can roast and eat these. The nice, big, plump seeds are the good ones. Once they are clean, let them air dry really well.
Store in an air tight container like a glass jar. As with any kind of seed, try to save the seed from multiple plants, not just one. That way you have a good variety of seed to plant. That’s it. Seeds all ready for next year (for free)!