How do I build a cat tree for my cat?

First thing take into account the size of your cats. I have a very large cat 23 lb. No Ordinary shelf will hold him as he jumps up there. So be sure your shelves are secured very well. Remember cats like to be high up to survey their Kingdom. They will often take naps where they can see the entire room or out the window. Your top shelf should be wide enough for the cat to sleep on without falling off. You may want to consider putting a railing on the shelves to help in this case. You may want to put some of the shelves where a cat can look out the window. Bird watching and seeing who's coming are very important to a cat. Also if you have a vertical beam or support in the room you may want to wrap it at least half way up with sisal rope. This gives them a scratching post and the simulation of climbing a tree. My best advice is to Google pictures of cat friendly rooms you will find many Inspirations there. But always take into account safety I have seen some that don't look safe especially if you have two cats sleeping on the same shelf or a very large cat. Also position your chairs where you can watch your cats it's a lot of fun to see them up there.

Cats like to climb. It does not need to be expensive. My son just made a shelf extension for his cat covered with soft carpet.

We made one with a solid base and a few steps with a landing pad Uptop. We used scrap wood and covered with carpet before nailing them together. Heck, even a cardboard box works for cats with a cut out to poke through.

Here's a bunch of great ideas https://www.google.com/search?q=making+a+cat+friendly+space+with+shelving&rlz=1C1CHBF_enUS750US750&oq=making+a+cat+friendly+space+with+shelving&aqs=chrome..69i57.18532j1j7&sourceid=chrome&ie=UTF-8