There are models that you can fold up and simply wash in the washing machine, just make sure you check the label or washing instructions on the packaging so you know how many degrees you can wash your cat tunnel at.
If you can't fold your cat tunnel and wash it in the washing machine, read the package insert carefully as it will tell you exactly how to wash the tunnel. Basically, if it is made of fabric, you can always carefully remove cat hair with a hoover or clean it with the right cleaning agent for the fabric.
Cat tunnels made of polyester can usually be washed with water. Just make sure, if you use a garden hose, that the jet is not too strong and does not tear your cat tunnel.