In addition to the pet-specific aspects: Learn the basics of photography first. Practice also on easier, stationary subjects. It’s easier to figure out your framing and such when you don’t have to time an expression or follow motion.

Creative Live, Coursera, LinkedIn Learning among others have good courses. YouTube will require sifting through the people who don’t know what they’re doing. Search terms might include “getting started with photography”, “intro to photography” etc.

Hold a feather toy just above your lens to get them to look right at you.

Try to stop down your aperture to maybe f/8.0 or so. You’ll need more light to do this, but pets tend to have longer faces than humans, and it will give you more room for error on focus. It’s a common problem to be focused on the nose instead of the eyes, and on humans this isn’t as noticeable because we don’t have snouts

If you make use of a leash (or arm) to help with herding (or branch out into other critters), take a photo without the human or critters in it also to help with removing the human and leash in post.

I’ve mostly photographed dogs, like others have said get down on the ground to their level. Have someone behind you to get the pets attention. Remember they each will have their own personality. My sister has two dogs, one is camera shy, if she sees a camera, she’ll sneak off to another room. The other will roll over onto his back, very submissive. My niece has a dog that will pose when you get the camera out. Crazy! Good luck.