More is a quantifier. It can be used directly before a noun or noun phrase.

I need more time. (NOT I need more of time.)
Would you like to have some more cheese? (NOT Would you like to have some more of cheese?)

Before a noun with a determiner (e.g. the, my, this etc.) we use more of. More of is also used before pronouns.

You are more of a fool than I thought.
Five more of the missing miners have been found.
Could I have some more of that cake?

More of can also be used before personal and geographical names.

I want to see more of Britain.

One more, two more etc

The structures one more, two more etc., are used before noun phrases.

We have one more task to complete.

More is also used to form the comparative forms of longer adjectives and adverbs.

Beautiful; more beautiful
Careful; more careful
Attractive; more attractive

Most

Most is the superlative form of more. It is used before a noun without a determiner.

Most people love babies. (NOT Most of people love babies.)
Most cheese is made from milk. (NOT Most of cheese is made from milk.)

Before pronouns and a noun with a determiner (articles, possessives and demonstratives), we use most of.

Most of us like movies.
Most of the people here know each other.
You have eaten most of that cake.

Most of can also be used before personal and geographical names.

Most of Mumbai was under water. (NOT Most Mumbai was under water.)

In comparisons most is used with the.

Which country produces the most milk? (NOT Which country produces most milk?)