Roses respond very well to pruning out old, tired canes. Older plants will send out rejuvenated new growth and flowers.  This short video from Saturday's Garden time https://www.youtube.com/embed/cAPNwJwhfvk  from a couple of years ago shows the Rose Society's curator pruning roses in the test garden, just to give you an idea of rose pruning basics.

 In the fall the goal is to just to trim long branches that will be damaged in winter winds.  Wait until the leaves have been shed and you can see the structure more clearly. Any branch that is pencil width or less should go - they are too weak structurally to survive the winter.  Cut any long branches back to the scaffolding.  Then wait until spring for a more extensive prune.

Spring is the time for major pruning.  With climbing roses form and structure are all important.  The first step is to evaluate your rose plant.  Prune out all small canes, and remove canes that cross each other (the rubs create injuries) so you can see the basic structure and form of the plant.  Look at the framework canes of the rose, the large canes that determine the form of the plant.  You will want to reduce the number of these large scaffolding canes to 3-5 eventually.  Identify canes that are old and probably not producing many flowers and remove them with a pruning saw at the base.  If your rose is grafted be careful to prune down only to the graft.  Now look again at your plant for balance and form.  Keep young, strong canes (they will have smooth green bark with visible growth buds) that are in a location on the rose that you want to keep.  Prune out canes that are in the wrong location or are no longer producing flowers.  Get down to 3-5 scaffolding canes. 

Portland Rose Society  http://www.portlandrosesociety.org/all_about_roses.html schedules pruning demonstrations of roses in the spring on their event calendar.  Check in February for dates of live demonstrations.   Meanwhile, these articles, Spring pruning guide  http://www.portlandrosesociety.org/f/PRS_PruningGuide1.pdf and How to prune roses.https://www.heirloomroses.com/info/care/how-to/pruning/. give extensive basic information on pruning roses.  Just remember to take a step back and evaluate your rose while you're pruning, and be brave, roses are really very forgiving.