They need to fully mature and get hard like a winter squash. So if you save seed from them now, it will be no good. I'm not sure how long you have to wait for them to be fully ripe, but it will be a bit of time still.
Remy

Also, if you have more than one type of squash and they are openly pollenated, won't the seeds potentially be some mutant cross??

Tak2w,
Yes, they could end up being a mutant cross. I figured the poster would decide against saving the seeds(though I could be wrong) and didn't go into more detail.
Remy

Mature zuc will turn orange usually. The skin will be hard as a butternut. When the vine is dead like a pumpkin the seeds might be ready.

Remy..so glad this subject came up as somebody gave my sister what she said is a yellow squash from their garden and my sister said the squash, even though it is yellow, is so hard, she couldn't even cut it. Does that mean that it is not a summer crookneck squash or it's not ripe? The person that gave it to her is a first time vegetable gardener. Could it possible look like the familiar summer yellow squash and be a different type?

Pippi,
Without actually seeing the squash it is hard to say for sure. But if it looks like a yellow crookneck, it could be that it is maturing to the seed stage. This would make it get hard and the seeds within would be hard. It could also be some strange environmental thing if the squash still seems immature.
Remy