Saving green bean seeds and cucumber seeds

(1) I have two types of green beens vines growing next to one another; will the seeds be crossed? (2) When and how do you save cucumber seeds?

There's a chance for crossing on your bean seeds. Most beans will pollinate themselves with little help from insects. The pollen is not wind-borne, it is transferred by vibration of the plant or insect borne, so the chance is there if a bee happens to visit flowers on two different cultivars.

Cuke seeds are saved from the big, overgrown yellow or mustard colored or gourd like things that cukes grow up to be. Seeds are not viable in the eating sized cukes. You scoop out the contents of the cuke into a cup and add about as much water as you have gunk. Let it sit for about a week and ferment. This gets the gel substance off the seeds. You rinse in a strainer and let dry for two or three weeks before storing.

Melody, THANKS SO MUCH! I haven't had too much time to research, and hoped for a quick and easy answer, which you kindly offered. So I should wait until my mustard colored cukes get larger, but not beginning to rot?

When they are almost gourd-like, it's time. They won't be 'woody' like a gourd, but they'll toughen up considerably.

At this point, you'll have a great number of viable seeds, and frost will ruin the fruits. Just judge when to harvest, and go ahead and go for it. If the vines are dead, or almost dead, they're ready.