Use a universal needle. If you are using a ball point, sometimes that creates a rip in the elastic instead of slicing through it just to create a hole for the thread.
Make sure you are using "lastin" brand and not just "clear" elastic. The stretchrite stuff called "clear" elatic is awful.
use a 3-step zig zag.. so you aren't putting too many holes close to gether in the elastic. If you can get a width that goes off on one side, through the middle and then off on the other side, that's ideal because it will hold the elastic in place without creating too many holes.
As for pulling.. you want to pull until the elastic stops giving readily.. stop stretching it at the point that you have to use effort to stretch it more. Lastin will keep stretching quite a bit beyond that point, but beyond that point, it will cause too much friction on the thread and the thread will literally cut through the elastic .. no or in a few uses. It also causes it too be too tight. It's soft of a fine line, but if you stretch it a few times before sewing with it to get a feel for when it sort of "catches" and becomes more difficult to stretch, you'll feel it when you are sewing.
Hope that helps some. I really adore the fit lastin can give when sewn correctly. I think a lot of the bad rap that lastin gets is because it's more difficult to sew with and sewn incorrectly, it's really awful.You've done it before though, so give it another chance and maybe it'll come back to ya