Hi Pippi,
They are easy to get seed from, but you must let a few flowers completely die on the plant. You can't dead head them and try to saved seeds. The dead flowers do look a bit unsightly, so dead head most of them and leave ones that don't stand out too much for seed collection. The link below shows everything you need to know.
Remy

Here is a link that might be useful: Shasta Daisy Leucanthemum x superbum Page

I just harvested a neighbor's shasta daisies(I think the variety is Snow Lady or _____?____Princess, with the permission of her landlord. If I pot some up now, do you think I could summer sow them now and they'd be ready to transplant by mid Sept. for a plant swap?

Well, if they pop up quickly, they will still be dinky, but people may take them.
Remy