I compost for the same reason you’re thinking about it, my vegetable garden. Plus it cuts down on what we send to the landfill (do you know how much you can add to a compost pile just by preparing veggies for a stir-fry??)
It’s easy, not a lot of work and, as long as you don’t put in stuff you’re not supposed to, it doesn’t smell – well ok, a faint smell of decaying leaves.
You can buy compost bins but I’ve had one and didn’t find that stuff broke down very fast. When I moved I didn’t bother with a bin.
I just found a nice sunny, fairly well drained spot in my yard.
Marked off a patch about 2 feet square.
Bought wire mesh (you could use chicken wire but I went with wire cloth as I find it easier to work with) and some tall metal plant stakes.
Planted a stake at each corner of my patch, wrapped the wire mesh around them and zip tied it to the stakes in a few places. Left one flap free for a ‘door’.
Inside the enclosure I placed 3-4" leaves and started layering leaves/grass clippings and kitchen scraps (veggie peels, tea bags/leaves, coffee grounds/filters, egg shells, stale bread, etc.) NO MEAT, FISH OR FAT
We have a fairly big yard so a regular mowing will usually produce 2-3 bags of clippings which my compost pile loves. You will find that if you leave the clippings alone and don’t disturb the pile too much it will heat up nicely and start to cook. That’s just what you want. Keep layering and every couple of weeks turn the pile, mixing everything up. Composting is as simple as that.
We have temps of -20 in the winter so I just keep a big garbage bin by the back door and in it go all my compostables. In the spring I just drag the bin to the compost pile and dump it, mixing it with leaves that I’ve kept from the fall. The frozen compostables break down quite quickly.