How does a home equity line of credit work.?

If you're in Texas you can borrow up to 80% of the value. In most cases there are no closing costs. The line of credit is available for you to draw on and until you do there is no interest. You can draw against it, pay it down and then draw back up if need be. Ours are interest only for 10 years and then become amortizing at that point.

Do you pay it with your mortgage payment?

No, separate loan unless you use it to pay off your mortgage.