With our only pet being a cat, it is pretty much the same as what I would do for a small toddler. Keep cabinets closed that contain dangerous materials, and certainly keep things that can fall off away from the edges of tables, counters and such. If you use pesticides for any reason, make sure the product is placed in an area that your pet can not access. Also, we burn a lot of candles. Candles left unattended can become quite a danger with animals running around.
Also, safety would involve screens on windows, door and such. Holes in the fences or under the fences.
Pet proofing a home is similar to thinking about how children explore your home. Pets are curious creatures and will venture into spaces, holes, hidden areas in your home. Our cat used to hide underneath the Christmas tree every year. I guess he felt it was close to being outdoors; so, we had to make sure all glass bulbs were higher in the tree and watch for his playing with the cords. I would provide the pet with altnernative spaces such as pet trees.