All the parts in this instructable were being thrown in the trash by other people.
1 Large cardboard tube. The one I used was from a carpet roll that was being thrown out.
1 Large flat piece of wood to form the base. I found a cupboard door on the street.
1 Chunky bit of wood for the upright. The piece I found was ugly and full of nails but nobody will see it, so it doesn't matter. Needs a flat bottom so saw it if necessary.
1 Self tapping countersunk screw.
Corrugated carboard - optional. This was some packaging material that was getting thrown out at work. Choose whatever your cat likes to scratch. I guess carpet offcuts would also work.
You will need:
Hand Saw (you could use a knife if you were VERY careful)
Glue for cardboard (I used a glue gun)
Small amount of duct tape
Step 1: Attach the Base to the Upright
Mark the centre of each piece of wood with a pencil and drill some small pilot holes for your screw. I used a 2mm carpentry drill bit.
If you have a countersink bit (I don't) you should countersink the hole on the base. Make sure you raise the flat piece of wood off the ground or put some sacrificial wood underneath so you don't drill into your floor.
The holes should go right through the base and a few cms into the upright.
Once you've got these holes screw the screw into the base so that it protrudes about 5mm-10mm from the other side. Now lines up the screw with the hole you made in the upright and twist it by hand, so that you are scewing the upright onto the base.
Once it doesn't turn any more finish scewing the scew into the base until the head is flush with the wood (or close as possible). This should make a pretty sturdy connection between the base and the upright. If you like you can cover the head with a bit of tape to avoid damaging your floor.
Step 2: Mark and Cut the Tube
Place the end on the base mark the desired height with a pencil and cut with a hand saw. If you don't have a saw you can use a knife but BE VERY CAREFUL as the knife could get stuck in the cardboard and fling out when you pull it.
When you are cut the tube place it over the upright. If it doesn't fit too well, you can tape / nail some scrap bits of junk wood on to help secure it. You could even nail the cardboard tube to the upright. It's up to you. I don't think it matters to much to my cat if it wobbles a bit.
Step 3: Put a Cover on the Tube
Remove it from the base and upright and cut your cover to the right size. Then using glue (I used a glue gun) wrap the cover around the tube. Trim the excess with some scissors.
They'll probably ignore it for awhile then refuse to pose for photos. That's cats...