The most expedient way of making targets is to get slices of some large diameter logs. Areas that are being cleared for construction are a good resource. Also check out local saw mills to see if you can scam some slices. Ideally the slices should be 2 or more feet in diameter with each slice 6 or more inches thick.
If you cannot get log slices another possibility is sandwiching common lumber together to make the target. This has the added benefit of allowing you to make very large (and heavy, not that a 12 inch thick 2 foot diameter slice of oak is light) targets. Start with any 2 inch or more thick lumber you can get cheap. use wooden pegs to sandwich them together or attach them to an 'A' frame backing. Targets can be made quickly this way, but they have two drawbacks. First, a good days throwing will make lots of kindling. Second, they present the 'long' grain to the thrower. If the weapon doesn't strike the target in the direction of the grain then it will have a harder time sticking in, and will make bounce outs and ricochets more unpredictable.
Using 4x4s (or lots of 2x4s) targets that present end grain to the thrower can be made. This is done by mounting 6 inch slices of the lumber in a frame designed to tightly hold them together. I've never made a target like this but it seems quite feasible. The only difficulty is in making the frame. It must maintain the tension desired without using any exposed metal that can damage weapons. With such a target you could actually disassemble it from time to time and replace just the slices that are damaged.