How to Install a Cat Door in an Exterior Door - By a Novice 

The problem: how to give our cat, Lily the freedom to leave and enter our house without our assistance.
The solution:
Step 1: install a cat door in our kitchen exterior door that opens into the garage. Since Lily is accustomed to exploring and napping in the garage, it made since to give her access first to the garage. We could leave the garage doors cracked open for Lily to exit and enter into our front and back yards at will.
Step 2: if step 1 works well, install a second cat door in the exterior garage man-door that opens into the backyard.
Background:
When Diane and I brought Lily, our Flame Point Siamese kitten home from the Olympic Peninsula Humane Society in August 2018, 3+ years ago, we thought that she would be an indoor cat. But during her first year with us, we couldn’t resist introducing her to our fenced-in back yard and beautiful gardens. And Lily took to the exciting world outdoors like a bird in the air. We were conflicted over allowing Lily the freedom to go outside unattended, knowing the risk of the busy road in front of our house, the local wildlife including hawks, eagles, raccoons, coyotes, the many local deer, not to mention feral cats and loose dogs. But Lily always returns home, and still does, to get a meal and treats, drink some water, take her daily afternoon naps, snuggle with us in bed overnight, and of course to get tons of love and attention from us.
For two years now, we have allowed Lily independent access to the outdoors by keeping the kitchen door to our garage cracked open, securing the man-door to our backyard open with a bungee cord, and keeping the garage door raised high enough to let her enter. This worked well, but at the expense of cold or hot air entering our house, along with a reduction in the security of our home.