Best "how to" way of hanging heavy curtain rods securely?

Hollow wall anchors, also called wall mollies. Shown below. They come in different length for different thickness walls. Get the ones for 1/2' walls if you have drywall. If you have plaster walls drill a small hole so you can measure the thickness of the plaster. The second pic shows what happens behind the wall when you tighten up the screw.

Drill small hole at desired location. Insert anchor and tighten screw until anchor is clamped in wall. Remove screw and put through bracket and reinstall. If you hit a stud when drilling forget anchor and just use 1 1/4" #6 sheet metal screw.