The most important thing is putting your animal partner first...this means being clean, clipping fingernails, etc. so that you don't give them an infection or scratch them. Hopefully this is with an animal who knows you well and whose body language you can read, as it's otherwise harder to tell what they're enjoying or not (and this is just one of many reasons why fence-hopping is a very bad idea).

Essentially, just take things slowly, use lots of foreplay (and water-based lube if necessary), and if you know or even think the animal is uncomfortable or in pain, STOP! Respect their wishes, above all else. Other than that, have fun!

Horses and dogs are very different animals. Male and female dogs and horses are also pretty different as well — get more specific and we can probably give you better advice.