When you have an active cat that needs some place to hang out outside, one option is to build a cat tree that can survive the elements. One way to do this is to use materials that came from the outdoors, since you know they're going to be able to weather most storms that get thrown at them. If you have access to a forest near your home, the job won't cost you much in materials. To complete the task, you'll need some basic tools and carpentry skills.
Use a hand saw or chain saw to cut a limb from a large cedar tree that is about 8 inches at its thickest point, and anywhere from 4 to 6 feet long. Try to choose a limb that has smaller limbs springing from it that will act as "steps" for your cat. If you don't have access to cedar, you can use another type of wood -- cedar just smells nice and is soft enough that it won't splinter on your cat's claws.
Cut the smaller limbs off, using your hand saw, so that some of the limb is left on the trunk and each small limb sticks out from the main trunk 8 inches or less. If you didn't cut the bottom of your main limb very flat when cutting it from the tree, use a hand saw to cut it evenly now, so that it will sit flat on the base you're going to create.
Peel the bark from the limbs and trunk, if you desire to have a smooth look for your cat tree. You can also leave the bark on and let your cat scratch it off over time. If the bark is tough to remove, use a paint scraper to scrape it off.
Sand the ends of the limbs and trunk where you've made the cuts. This is especially important for the bottom of the trunk, where it will be attached to a base, and the top of the trunk, where you'll add a perch. If you've peeled the bark, now also sand the trunk to create a smooth finish. This is where an electric sander can really come in handy, as you may have a lot of trunk to sand. Start with a medium-grit sandpaper and work to a fine-grit when you've smoothed out the rough stuff.
Attach your 1-foot-square cedar plank to the top of the trunk with a screw. If necessary, drill a hole through the plank first and then secure a screw through it and into the trunk. This plank will be the cat's perch.
Cut a 2-inch section from each piece of 2-foot 2-by-4 using your hand saw, so that the 2-foot pieces now measure 1 foot 10 inches.
Build a base for the trunk by placing one of the 2-by-4s over another one of the same size, in a cross fashion. With the pieces held in place, use a drill to make a hole through the top board of the cross and then join the two pieces with a screw.
Add pieces to level the cross. One board will be higher than the other and thus the base will not sit level at this point. To deal with that, take the two 2-inch pieces of board you cut from the 2-by-4s and secure one to each underside end of the higher ends of the cross. Drill a hole through the 2-inch piece, and then secure a screw through that piece and into the underside end of the two sides of the cross. When this is done, your cross should sit level on the ground.
Secure the entire cross to the bottom of the trunk by drilling two holes through the centre of the cross, and then inserting a screw through the holes and securing them to the bottom of the trunk. For further security, you could use a bit of wood glue between the base and the trunk.
For more fun for your cat, you can add "shelves" onto the limbs of the trunk. To do this, drill at least two pilot holes through a 1-foot-square plank and then use screws to join the shelf to the limb.