I bought a pair of casual shoes yesterday and they [ the shoes] fit me perfectly.

A shoe is one piece of shoes. One shoe = it. Two shoes = they. Possessive adj (This, That, These, Those): One shoe = this shoe, that shoe. Two shoes = These shoes, Those shoes A pair (of shoes) ["pair" is single(1)] = This pair of shoes, That pair of shoes Two pairs (of shoes) = These pairs of shoes, Those pairs of shoes In your sentences, 1) I bought a pair of shoes. How do I count (them)? ["Them" because you are asking about pairs of shoes in general. All shoes. How do I count (pairs of shoes)] 2)I bought a pair of casual shoes yesterday. (They) fit my feet. ["They" because each shoe goes on each foot. Once you separate them, they become 2 shoes again instead of a pair (because pairs belong together)

Shoes are plural, but a pair of shoes (2) is singular. So, you can say "This pair of shoes fits me", and "These shoes fit me".