Deramaxx is still available for dogs. We usually use that or Rimadyl for post-op spays and neuters. In tiny dogs, we use Torbutrol.
The dog should be given an injection of pain medication before it is totally awake.
Torbutrol and Buprenex and a few other pain meds can make the dog sleepy. Rimadyl and other NSAIDs do not.
A spay is abdominal surgery, so they usually do need pain meds for a few days. Within 2-3 days, though, the dog has usually bounced back completely. It is very important to keep them quiet for the next week - no running, jumping, rough housing, etc. If those sutures go, you have an open incision into the abdomen. So, follow your vet's confinement instructions.
Most clinics where the policy is that they stay overnight require you to make arrangements with the vet before hand if you want to take them home the same day. Many vets are very hesitant to do this because of lack of owner compliance in general with post-op instructions. Basically, the dog should come home and be crated for the next day with only brief leash walks for potty breaks. Keeping them overnight ensures quiet confinement.