1. Keep your pet confinedThere are many anesthetic drugs available, and animals can react in a number of ways, depending on their age, weight, general health, species, and breed (in some cases). Just because your cat came home from her spay last year running around as if nothing happened, doesn't mean that your other cat will come home from his dental the same way. Keeping your pet calm the first 24 hours will speed anesthetic recovery and restricting activity for several days will help prevent a surgical dehiscence.
2. Make sure your pet is warmIf your pet is still a big groggy, s/he may have trouble maintaining normal body heat. If the animal is normally an outdoor pet, it is wise to bring them inside if the outside temperature is cool. Indoor pets may benefit from a comforter or pet "snuggler" bed. Do not put your pet on a heating pad unless directed by your veterinarian. This can cause severe burns if used improperly!
3. Monitor the food and water intakeHow soon your pet can eat and drink will be determined by your veterinarian and what procedure(s) your pet had. While it is encouraging to see your pet eat and drink (especially after the pre-procedure fasting), please do not offer more than your veterinarian recommends! This can lead to an upset stomach and vomiting, which isn't pleasant for you or your pet.
4. Remove obstacles and hazards for your petAssuming that your home/yard is already pet-proof and safe for your pet, take an extra moment to consider things anew. Your pet may not be completely "with it" as far as depth perception, coordination, and judgment for several hours after they are home after an anesthetic procedure. This can result in injury from common things; such as stairs, chairs or other physical obstacles. A dog or cat crate may be the safest option.
5. Be careful handling or moving your petEven though most veterinarians do administer pain medications, your pet may be in some pain or discomfort as the anesthesia wears off. This can cause an overreaction to "normal" things, such as jumping up on the bed, being picked up, or going for a walk. Move a little more slowly and carefully the first few hours after your pet is home to ensure that they can be handled as they normally are. If your pet is wearing a splint or bandage, be sure to use extra caution for normal activities.
6. Supervise pet-to-pet interactions upon arrival homeWhile humans may assume that the pets miss each other and can't wait to see each other again, this is not always the case. Pets, especially cats, may view the returning pet as foreign, due to all of the new odd smells and possible different behavior of the returning pet.
Conversely, exuberant pets may be "too much" for the returning pet; the excited greetings and playtime will need to wait until the anesthesia is completely worn off and sutures (if applicable) have healed.