when i had my siamese spayed i was really worried that it was going to be like when i had my dogs spayed.
i couldnt believe how quickly she recovered, the only difference in her was that she was very sleepy, i kept her in a quiet room away from my dogs, i let them say hello to her but then put them out of the room.
i stayed with her and kept a close eye on her until she had fully come round.
She will be allowed water, and try to get some plain chicken, feed her tiny amounts a few hours after getting her home, as she could go off her food, plus it will help her to come round a bit quicker, dont feed her to much as she may vomit.
The following day she will probably do what my cat did, and started strutting her stuff around the house as though nothing had happened, we actually put a collar on her to try and slow her down, not from fear of her biting stitches, just so the cone would stop her from jumping around like a nutter!
As regards your dog, if its a boy, then the operation is very minor.
If its a girl, then my advice would be to allow her to have her first period, i have two girls and from two seperate vets they both agreed on them waiting for them to have a period as it allows there hormones to settle, it is also supposed to help calm them later on in life, girl dogs who get done prior to having a season tend to be a bit flighty and giddy, whereas after they can be a bit calmer.
Spaying in dogs is a bit more stressful than a cat, but it all depends on the individual dog.
They will give your dog a course of painkillers and probably give them a long lasting antibiotic injection. they will be a little stiff and sore but after 2-3 days they should be back to normal.
If it where me and the 11 week old pup is a girl i would wait until she has her first period, contact another vet if you are unsure of your own, if you have had trouble understanding the vet, a nurse at the practice will be more than happy to explain/answer questions that you may have about the procedure etc, if they are bit funny with you then just change vets.
hope this helps a little.