If something is not too big and not too small for a person or other thing, it fits (them): A size 12 dress should fit. | You can't put those shelves in there, they won't fit.
If clothes or other personal things are the right style, colour etc for someone, you say they suit them: Casual clothes really don't suit her. | A green dress won't suit me. | That new haircut suits you!
Schools, places, times, situations etc may also suit people: A management position would suit him down to the ground. | California doesn't suit everyone. | Will ten o'clock suit you?
If people fit in they have a good social relationship with the other people in a group, and share the same attitudes, interests etc: Laura fits in perfectly at the tennis club.
If things are almost the same in some way and look good together, they match: The curtains don't match the carpet (= they are not the same pattern/colour).
If things look right together in style, colour etc, they go together or go with each other: The curtains don't go with the carpet (= they are not the same colour and do not look good together either).
Things can go together in other ways too: Fish and white wine go particularly well together.
In British English the usual past form of fit is fitted, but in the first meaning you can also use fit in more informal English: Two years ago, these pants fit me perfectly.
In American English, the usual past form is fit, but you can also use fitted for all the meanings.