Canyoneers use friction all the time when canyoneering. Here are some basics before we explain how they can be used in canyoneering.
Application 1 - Rappel Devices
When you rappel, the force that slows you down is the friction between the rope and the rappel device. When you apply a downward force to the brake strand, this increases the normal force or contact pressure of the rope on the rappel device. So as you pull down harder, it adds more friction.
After a long rappel, you will notice that your rappel device gets very hot. Be careful that you don't melt your rope or burn yourself.
Some rappel devices like the Critr or Sqwurel or ATS have additional horns or grooves which you can wrap the rope around. As you add more wraps and the rope has to bend around those edges, it adds more total normal force and consequently more friction. Per the Capstan equation, the frictional force is proportional to the sum of all the angles that the rope has to bend.
Some ropes have different coefficients of friction than others. You might rappel on one rope slowly and on another rope much faster. This has led to many accidents and injuries when a canyoneer isn't familiar with which friction settings they should use on a rope they haven't used before. For your first time on any new rope, it's much better to err on the side of caution and have a little bit too much friction.
Application 2 - Recovering from a Slide
If you lose control and start sliding down a slickrock face, the best thing you can do is walk instead of slide. This is just like anti-lock brakes on a car. Because the coefficient of static friction is higher than the coefficient of kinetic friction, you'll get more stopping force by making contact on the rock and moving your joints rather than lying down and dragging.
Since your normal force is just your weight, you're best off putting your weight on the part of you with the highest coefficient of friction. This is probaby the soles of your shoes but could also be jeans or some rough material.
Application 3 - Stemming
When chimneying, stemming, or bridging you use the friction of your body against the wall to keep from falling down. To increase the amount of friction, you need to push outwards against the two walls harder. However beginners will often push too hard because they're nervous and they'll burn out quickly.