FOR INFORMATIONAL PURPOSES ONLY. DO NOT TRY AT HOME!
WMD's usually consist of 3 categories:
Nuclear weapons:
Basically, you're gonna need to refine uranium ore into uranium metal and separate the heavier U-238 from the lighter U-235. Throw away the U-238 as it's basically junk (or make bullets out of it, it's some pretty dense stuff and is also pyrophoric and so is great for armor penetration but that's beside the point. It makes good armor too!). The lightest 0.7% of the stuff is the shit you want: U-235. That's your fissile uranium. Once you have that, you're gonna need to figure out the critical mass of the shit (government secret) and find a way to keep it below that before detonation and then quickly reach it when you want it to go off. The two most popular methods involve either wrapping a sphere of uranium in explosives so that sphere condenses rapidly and uniformly or the "shotgun method" which basically involves firing a cannon ball of uranium at another chunk of uranium and hoping for the best (the latter method being what was used on Japan). Duterium extracted from heavy water, which itself can be extracted from distilled water in much the same way you would go about extracting U-235 from uranium metal, can be added in a casing surrounding your fissile material to make it into a much more powerful hydrogen bomb.
Chemical weapons:
Basically, the goal is to disperse some toxic chemical as an aerosol or gas into a wide area. One way you could go about this is to take two containers: one of bleach, the other of ammonia, and bind them in a canister with some method to rapidly mix them after detonation. A small explosive charge will do depending on the geometry of your canister/containers. Use your head to come up with ways of dispersing it evenly and quickly. This produces chloramine gas (not mustard gas as is commonly claimed) which is a powerful lung irritant that can lead to permanent respiratory damage or death.
Bio-weapons:
Ask the Chinese. The one they've got going around right now is kinda shit but they're definitely on the right track.