I'll try to remember what I learned in my first year of college...
The type of pruning depends on the type of rosebush.
The ones that flower once in the season need to be pruned after blooming, so during the summer. The ones that flower continuously all season should be pruned in feb-march, after the severe frosts are over. Heirloom roses should be pruned less severely than modern roses.
On older bushes cut off the older branches at the base.
For the pruning itself, Becca is right in saying to make the cut at an angle. Cut it so that rainwater slides off the slope of the cut on the opposite side of the bud. Make the cut above a bud facing the outside of the bush.
Flhiker, I'm wondering if it's not too late to prune yours as it is already blooming. Normally it's better to prune before the year's growth has developed too much. But that's just my