Wondering what tools you need to work on a kart? The good news is you might not need much more than basic tools you already have. Almost all CIK style karts have metric hardware, and socket head cap screws are common, so you'll need some good tools to work with those. Here's what I usually bring to the track with some notes:

Basic socket set - A 1/4 sockets were recommended to me to prevent over-torquing, but I already had a 3/8 drive set so that's what I use. My set has metric (4-19mm) and standard (which I never use on the kart).

Additional sockets I bring a 21mm deep socket for the spark plug, and a 22mm socket to remove the front hubs (necessary if you want to change the front track width.

Socket Extensions 3 inch and 6 inch, necessary to get to lug nuts on the wheels.

Hex Keys/Allen wrenches I have 3 sets, which come in handy for different uses, although I don't always bring them all to the track. One is a long handle round ball end t handle set, which is good for speed and hard to reach places. I also have a shorter t-handle set with flat ends which is good for getting higher torque to tighten or loosen bolts, and a L shaped key set with one flat end and one ball end, which is pretty good for both.

Combination wrenches A basic set of wrenches with one open end and one box end, sizes 8-17mm

Air pressure gauge one which can measure to approximately a quarter psi is nice. One that only measures to 30 psi or less is also more precise/easier to read.

Tape Measure Necessary to measure the position of the hubs on the rear axle to change rear track width.

Rubber mallet comes in very handy for example to remove the rear wheel hubs from the axle, or remove the wheels from the hubs.

Screwdrivers I just use the screwdriver with changeable heads that came with my basic tool set. The only time I typically need a screwdriver is to take the airbox off to clean it or choke the engine to start it in the morning.

Tape duct tape and electrical tape

Pliers one needle nose and one channel lock style

Safety wire and pliers I've had to redo the safety wire when I've taken certain things apart, for example the steering wheel and brake caliper, although I've never actually needed it at the track. There are special safety wire pliers that help with spinning safety wire.

Flashlight self explanatory

Multimeter I bring a cheap multimeter since I have one, I have used it to check the battery voltage at home but have never needed it at the track.

Adjustable wrench a small one, don't think I've ever used it.

Files round and flat file. Never used them but might come in handy for something.

The more important/more frequently used tools are at the top of the list. I fit everything in one small toolbag. I also bring a box of spare hardware, and a box of spares parts/lubes/cleaners/rags. If there's something I don't have, I can probably borrow it from someone else, but I can't remember the last time I've needed something I didn't have in this list. If you don't have any tools at all, I think you could buy everything you need here, in a mix of cheap(aka Harbor Freight) and mid priced (aka Craftsman) for a few hundred dollars. You could probably add or remove a few things (especially near the end of the list) as you see appropriate. I also have a few specialty tools like a bead breaker and tire mounting tool which I haven't included here.