Initial Break In
As most people are aware, with new shoes there will often be points where the shoe contacts the foot and creates a degree of discomfort. The main thing to remember is that there should be no great discomfort as might be associated with a shoe which is sized too small. The normal contact point discomfort will typically be solved by proper break-in. The first step to breaking in climbing shoes is to wear them around the house. Doing this will help protect the bottoms of the shoes while enabling the shoes to begin the molding process to the foot. Wear them as much as possible and take extra time to do activities which will help stretch the shoes. For continual problems, you can try wearing a very thin pair of socks until the discomfort subsides.
Light Climbing
Wear the new shoes to an indoor climbing wall or gym. Also wear the shoes while doing short climbs or bouldering. The point here is to wear the shoes for short periods of time, which will help stretch them, and then take the shoes off, which will allow the feet to recover without developing blisters. Consider this as a necessary step and do not rush the process by skipping ahead. Short climbs give you the opportunity to stretch the shoes without damaging your feet by developing blisters which can greatly affect your climbing for the short term.
Climb as Much as Possible
As you begin to climb more wearing the new shoes, it is fine to give your feet a break by wearing an older pair of shoes. However, keep in mind that the new shoes will never become your go-to pair if they are not broken in properly. Progress to longer and longer climbs as you continue to break in the shoes. If you are still experiencing a great deal of discomfort, do not attempt to fool your self by thinking the new shoes can be stretched a half size or more. Due to the design of climbing shoes this most likely will not happen. Do not buy small with the idea that they will stretch out. Snug fitting shoes are desirable but not to the point of pain and discomfort.