I have had several foster dogs that are with me when they get spayed and now my own dog that was spayed just yesterday. Every dog that I've had that has been spayed tends to be tired and sore the first day and sleeps most of that day. They improve a lot after that first day.
Watch to make sure the wound isn't bleeding or looking sore/raw. The shelter should have given you aftercare instructions. But if not I'll list a bit here from the paper I got.
-Appetite should be normal after 24-30 hours. Continued vomiting, diarrhea or severe depression is cause for concern and you should call a clinic. Pets may have a slight cough which will go away.
-No bathing or swimming for 2 weeks after surgery. Incision must remain dry. Discrourage licking. An e-collar may be needed to prevent opening the surgical site. If incision opens contact vet immediately.
-No running, jumping or rough play for 7-10 days after surgery. Keep indoors. Do not allow dogs to play with other dogs.
-Check the incision at least twice a day. A small bump, redness or swelling may occur but should be minimal. Oozing, drainage and pus are NOT normal and usually means the dog is licking the area and must be seen to assess the damage/infection to the area.
As for how my own dog is acting right now. Yesterday she was spayed and when she got home she was very wobbly and tired. She slept almost the entire day. She barked once at the foster dog that is here (they were kept apart), and when she barked she whined in pain. I kept her away from stairs until time for bed then she had to go up a set of 13 stairs. She was hesitant, but she did it.
Now it's the next day and she's much improved. She ate this morning like normal. She's alert but still resting. On her own she has gone up and down the stairs a few times already. She jumped on a bed twice, which I don't think she should do, but I wasn't there to stop her. I have 3 days of pain meds to give her. The incision looks good so far. It's not red and there's not any blood. I don't see any stitches so I don't know what they did to keep the incision together. Maybe glue instead of stitches? I don't know.
Good luck to you both.