you can't teach cats. you can only give them options that they prefer over whatever it is you wish they wouldn't do. In our case, it is jumping onto the counter tops or shredding the couch.
We had one of those carpet wrapped "kitty trees" you get from the pet store, and while it worked it was filthy and unserviceable within weeks of use. at the same time, we have used these disposable cardboard "scratch pads" meant to be set onto the floor. Those work fine, but we feelt kind of weird paying $15 for one of them at the pet store. I wanted to put a simple construction together using the cardboard idea, while also giving them the height advantage to be able to look out the windows and keep tabs on the local bird population. Another climbing option might mean less time spent on the kitchen counter they seemed to like it okay
I based the design idea off of something I found googling around (and it can be yours for $435!):
Implementation was pretty straight forward. I started with two long sticks of redwood, bridle jointed at this angle: I then threw together some trays dovetailed in the moste expedicious way to hold things together. These were glued to the lateral supports using Titebond III, and a couple drywall screws for good measure. the glue is probably plenty enough, but screwing things together made the clamping process a lot easier. THere' was no real joinery between the two parts, just face glue, so they could move pretty easily even under full clamp pressure.
and then about an hour or two of cutting a bunch of 2" thick strips of cardboard, gluing them up to a thickness that will nest snugly into the tray frames. There were also some cleats I glued into the bottom of the trays to support the cardboard structure:
The lower stretcher is just a 2x10 with a few dados cut underneath to receive the "feet" of the structure. I wrapped some old rope to make a sufficient scratch pad.