If you put your compost pile on the ground, earthworms will come into it, you don't (usually) have to add them.
People do worm bin composting with tons of worms in a little bin, but that is a separate thing from regular composting.
The container is basically just a frame to keep your compost pile piled up and not blowing around the yard. It can be very simple. If you live in the city where there are rodents and raccoons, etc., your frame will have to be a little more secure to keep critters out. You can make them or buy them. There's lots of designs out there for compost bins from pallets:
here's a fancier more secure version:
or there are lots of plastic "earth machine" type bins:
or wire bins:
any of them work just fine, as long as there is enough air circulation.
Compost is for two main purposes: just to use up all your organic wastes, yard wastes and kitchen scraps, etc. so they do not go into the waste stream and have to be transported to landfills and take up valuable space there. AND because the finished product of a compost pile (called "compost") is a wonderful soil amendment. It has lots of nutrients, including trace and micro nutrients that are not present in commercial fertilizers. It has all the micro and macro organisms needed to continue breaking down those nutrients (and others present in the soil) to forms that the plants can take up and use. It has a beautiful texture which improves soil water management capacity -- adding compost to sandy soil helps it hold on to needed water better, adding compost to heavy clay soil improves the drainage so it doesn't stay too wet. Soil full of compost doesn't need to be watered as much AND etc.
It isn't fertilizer. It isn't as concentrated as fertilizer and the nutrients in it aren't available right away until it breaks down more. But the concentration isn't important. Commercial fertilizers you have to use very sparingly or you will burn your plants. Compost you can use by the shovelful and your plants will love it.
Personally, I started gardening because I had made a compost pile to keep wastes out of the waste stream and then I had to have something to do with the compost. I think compost is a miracle. Throw dead leaves and stinky garbage in a pile and (eventually) come out with rich, black, sweet-smelling, crumbly dirt. (And the garbage is only stinky before
you put it in the compost pile. A properly functioning compost pile has no odor, except a slight, pleasant earthiness)