Not every local pet store stocks stick insects, but if you ask then usually they can put some on order. However, if you are looking for one of the rarer species, or are seeking a high level of advice and support, then an entomological dealer could be the way to go. Entomology is the scientific study of insects, and there are specialized dealers in insects and the equipment that is required to keep them. Where to buy stick insects will depend on the species you are looking for.
You will probably want to start with a nymph (baby stick insect) given the short life cycle of these pets. A nymph that has been through a few molts is the best option as younger nymphs can be very challenging to see through to adulthood. If
your nymph has a few limbs missing it is nothing to worry about as these can regenerate, although that said if you have a choice then choose a specimen with the full compliment of limbs.
When you pick up your insect make sure you have a suitable box to transport them in, and keep them out of sunlight on the journey home. It is possible to purchase a stick inset via the mail, and if you select this option then ensure that the sender has had experience of insect postal delivery. The sender will need to provide enough food for the transportation and also mark the package clearly.
Just remember that wherever you buy you insect you need to make sure that you have the necessary food and environment for the species that you select.