Summarize:

Check for a pulse, and look and feel to see if she's still breathing. She may be in trouble but not actually dead. Call your veterinarian, and ask her to guide you with next steps. If your pet is still alive, take her to an emergency vet in the area. The best place to feel for a pulse on a dog or cat is the inner thigh, up where the leg meets the body. You're looking for the femoral artery. Use two fingers (not a thumb) to check for a pulse. You may have a hard time feeling it on a cat. If you feel a pulse, have someone time 15 seconds while you count beats. Multiple by 4, and you have the beats per minute. Your vet will likely want to know the beats per minute if possible. The body will start to decompose fairly quickly, usually within a day, so you want to bury the body as soon as possible. If you need to keep the body in your home, you can take a few steps to keep it from decomposing. You can wrap the body and put in the refrigerator, though you still want to take action within a day. You can also place the body in the freezer, which will keep it from decomposing longer. If you can't use either of these options, leave the body unwrapped on concrete, as it will draw the heat out. In your grief, you may not remember everyone you need to tell. For instance, it's important to notify kids who were away at college when the pet died. You also need to find a way to tell your children if you have young ones in your home. When telling kids, try not to use euphemisms. For instance, saying the pet has been "put to sleep" can be confusing. Tell the child that the pet died, and explain in simple terms what that means. For instance, you could say, "Honey, I have something sad to tell you. Our pet Kitty died today. That means that she stopped breathing and her body stopped moving. She won't be coming back to live with us." It can help to let the child see the body, though it's okay to soften the blow by covering the body partially with a blanket or putting a beloved toy nearby. Answer any questions your child has as honestly and directly as you can, though you can say you don't know. Also, be prepared for the ways your child's grief will appear. Some children will want to write letters or leave flowers. Others may want some alone time, while still others may need more cuddles. Letting your pets observe the body, sniff it, and interact with it can help give the pet closure. If they can see the dead body, they may not spend as long looking for the pet to come back after she's buried. You may or may not be allowed to bury your pet on your own property. It's typically not okay to bury in a public park, but sometimes you can bury your pet on your own property. Try calling your vet to see if she knows the local law. You can also ask your local humane society. If you're still not sure, try calling the local police department to ask. Once you know whether you're allowed to bury your pet in your yard, you may decide to bury her there. However, you do have other options. For instance, some cities have pet burial parks where you can buy a plot for your pet. To find a pet cemetery, ask your vet. You can also look under "pet cemeteries" in your local area. Another option besides burial is cremation. Some vet hospitals have cremation services, while other times, the crematory is a stand alone service. Be aware that you may have the option of individual cremation (where you just get your pet's remains back) or group cremation (where your pet is cremated with other animals). Individual cremation is more expensive.
Check your pet. Take action within a day. Notify people. Let your pets see the body. Check your local laws. Decide on a burial spot.