I've been most successful out here on the west coast trail running, not climbing. So for the benefit of others I will describe how I have learned to conquer trails faster. For Attitude (Part 1) click here.
This tutorial begins at the ground. Like any good machine it is built from the ground up. The first step in going faster is your choice of footwear. While there can be some discussion about the perfect footwear the fastest choice is lightweight running shoes. In the past two months I have carried 60 pound backpacks with lightweight running shoes, I have free soloed 5.0 rock climbing, and ran for most of 31 and a half hours. All with the same pair of shoes.
Backpacker Magazine several years ago put out a article about lightening your load so that you could save energy and hike farther. One of their pieces of information was that one pound of weight on your feet is like carrying another 6.4 pounds on your back (page 51). The idea is that you have to move your feet a whole lot more than the stuff on your back gets moved. That is to say that if you can make your footwear two pounds lighter you could carry over 12 pounds more gear in your backpack and still burn the same amount of energy. Alternatively, you could simply save the weight and hike a fraction of a mile per hour faster and an hour or so longer than your previous backpacking.
I realize that running shoes are not for everyone or every situation. Approach shoes, street shoes designed for climbing, are designed for climbers tackling fourth class or easy fifth class terrain so that they can approach the difficult section of the climb without having to stop and change their shoes multiple times. However, when the climbing is never very difficult they can simply use the approach shoes for the entire route instead of even bringing climbing shoes, saving more weight. The more technical the terrain the more sophisticated gear that will be necessary to cross it. Steep ice climbing will require boots, crampons, and ice axes.
Getting back to simple non-technical trail, keep in mind that the goal is speed. Now imagine that you can only burn so many calories in the course of a day. The less weight you are carrying the easier it will be. Lighter shoes are the way to go. I recommend going for the lightest running shoe you can find that offers you enough support. I am a fan of minimalist shoes so the shoes I have been trail running in this summer are Mizuno Wave Ronin 2s which come in at 8 ounces and are advertised as racing shoes. I think they are actually partly responsibly for my stress reaction, but they have a very nice, fairly durable tread which is better than the other seven pairs of lightweight shoes I have. The point being, a good tread is important. Trails have wet rocks, mud, sand, stream crossings, polished logs, and moss that all conspire to reduce the traction between your shoe and the ground. So whatever shoe you go with bring something that won't fall apart after a few miles.
Be sure that your shoes and socks combination works for you without giving you blisters. Going up and down and around switchbacks will throw your feet around your shoes like crazy. I feel that I am more likely to get blisters on these runs with difficult terrain than I am pounding the pavement. With proper shoe fitting and a nice pair of socks you should be fine. Although, there are no guarantees.