First of all take a deep breath. Pets are work and so if you're going to have them realize they do more than look cute and keep you company. They require a bit of upkeep but it is in everybody's best interest so don't despair too much. Just make time for it and add it to your list of to-do's.
If the cause of the pet odors are things like cat litter or pet messes then you need to clean this up. Clean up the cat litter as soon as you can. If while you’re at work and they perfume your home scoop in the morning before you step out of the house and first thing when you arrive home. Dispose of used cat litter in your outside garbage can. I will say I used the Litter Locker cat litter disposal system with good success. We had two cats in a small space and this would contain odors for a few days fairly well.
If you have pet messes do your best to clean them up. Scoop and dispose of solids. Damp up as much liquid as possible. Treat with an enzyme cleaner and I highly recommend the 123 Odor Free Kit. And it works on hardwood floors too (my friend alerted me to this fact after she bought a kit for her hardwood floors upon my recommendation). You can read my review here.
Next up find your pet’s favorite sleeping place and make sure it’s a washable one. For example my cats loved our bed. They would lounge there for the whole day. We purchased two washable throws and I wash them every other day or so.
Use fresh air. You'll find it does a much better job than canned air or some scent you spray around. Air your home regularly. Summer, winter, spring, and fall. Let air cleanse your home of offending odors on a regular basis. A good practice is to air your bedrooms each morning for 15 to 30 minutes as you can. You can do that with any room where your pets spend a lot of time.
Use a spring cleaning chore to remove odors and wash your walls. This can be time consuming so space it out over the year. For example wash the walls in one room on week, or even month etc.
Use a simple solution of a dash of dish washing liquid in a bucket of warm water, and another bucket with just water. Wash walls with one sponge, rinse with another and wipe dry. Test your paint in a small spot first to make sure it will not damage.
If you have a pet and carpet vacuum often. Daily. Pet hair can carry odors.
And of course keep your pet clean. You cat may have something to say about this but thankfully there are professionals who can deal with his attitude. Fido will enjoy the experience.