Outdoor Gear Stores
The best place to buy climbing shoes is an outdoor gear store with a trained staff who can help you find a shoe that fits and is appropriate for your excursion. A large outdoor retailer such as REI will typically have a good selection, but your choices at smaller gear shops may be limited. Simply trying the shoes on isn't going to allow you to evaluate how they will perform, so make sure the store has a small rock climbing wall to practice on. Try to get a feel for how the shoe grips the rock, and how much power you have when toeing down.
Online
If you can't find the shoes you want in a store, you can order them online, either direct from the manufacturer's Web site or from any number of sites that sell climbing gear. Maybe you tried on the perfect shoes in the store but want to find a better deal. If price is an issue for you, sellers on eBay list new or gently used climbing shoes starting as low as $10. Be wary of ordering a particular style you've never tried on before. Just because your climbing buddy loves a certain brand or style of shoe doesn't mean the same shoes will be right for you. You want to look for a toe box that mimics the shape of your actual foot to ensure a snug fit.
Your Climbing Gym
Your climbing gym will often be able to order shoes for you; some will even offer a discount to members. As with shopping online, it's best to order a brand or style you have worn before. If your climbing gym rents different styles of shoes, try a few different ones to find one you like before ordering.
Other Cimbers
Check the community bulletin board at your gym to see if any climbing shoes are for sale. Climbers will often sell new or gently used shoes ; If the shoes have been worn a few times, you can often get them for a good price.