when is the best time of year to trim my golden rod bushes and how far back should they be pruned?

Answer 1

If you have a forsythia bush, the best time to prune is when it is blooming. Cut out all branches without blossoms. After blooming it can be shaped. Later in late July or Aug. is another trim in order to make shape. It is important to cut out the old wood every 3 or so years (after blooming) and make room for new growth. Don't forget to remove non blooming branches in blooming season for an evenly yellow bush the following year. The cutting stems take forever to decompose, I recommend you drag them to the dump or where ever cuttings are collected.
Leaves can go into compost. :)

Answer 2

The golden rod I know of is an annual-- dies off in the winter and returns in the spring from the root.

There is a Forsythia which could be called a golden rod bush because it's branches are long and rod like. It also has blooms in yellow/gold that look like bells. The blooms are first-- before the leaves-- giving it a golden look. If you have a forsythia-- the time to prune is now-- assuming you are in the States-- otherwise, prune after blooming because the new wood is where blooms appear next year.
good luck