The first question you will need to ask yourself is whether you want to build a “historically accurate” traction trebuchet, or it’s simpler and easier to design and build cousin, the counterweight trebuchet.
If you’re building a trebuchet for the sole purpose of your high school physics teacher’s amusement, then you should probably consider one of the counterweight variety. If, on the other hand, you are building a trebuchet for fun or self education, the traction trebuchet may be something to seriously consider. (Keep in mind that at least three-fourths of the “free” plans on the web are of the counterweight flavor.)
Once you have determined your design plan, you probably want to decide on a suitable size. If your looking to launch bowling balls the length of a football field, you will want a much larger trebuchet than if your intending to launch eggs at incoming traffic. Which, of course, is a BAD thing to do. (Based on personal experience most drivers won’t enjoy chipping dried egg off their windshield.) Another point of interest is whether or not to buy premade trebuchet kits or design plans for your trebuchet. If you are just a beginner, kits are excellent to use. Plans also will help you out immensely if you are just a beginner.
Now, the next step is construction of your trebuchet. For most people, I would suggest using 1″x2″ pine for all of the pieces. But, if your going to be building a 10ft tall trebuchet, stretch for the 2×4’s. Once you have completed your trebuchet structure-wise, you will need to construct a sling and if used, a suitable counterweight. I prefer cutting up any kind of old cloth and attaching both ends to lengths of string.
Suitable counterweights can be anything from a box/bottle full of lead shot, to a sock full of rocks, or a dumbbell weight. After you have all of that stuff sorted out, you should attach the trigger mechanism and release pin. There are plans and pictures of these on most sites, but the only advice I can give you is that the release pin is the trickiest part of constructing a trebuchet. It should be angled so that the sling releases the projectile at an angle of somewhere around 45 degrees.
Final word: Building a trebuchet can be lots of fun and be a great learning experience. (Or sometimes an unbelievable chore for those unlucky physics students such as myself). Construct your trebuchet with quality and take care to add support where needed and it will last you a long time.