For "most" vs "most of" in general, here are some tips:
Use "most" if you are talking about an entire category:
"Most dogs are cute."
"Most people like to dance."
Use "most of" or "most of the" for groups with a limited size. Some specific examples:
Use "most of" with plural pronouns and possessive pronouns
Plural: "Most of us were happy." / "Most of them didn't win." /"Most of you are tall enough to do this."
Possessive: "He still has all of his money, but I lost most of mine."
Use "most of" with possessive articles.
"He wasted most of his money."/ "She likes most of their paintings."
Use "most of the" for any defined group:
There were 15 games in the contest, and we won 10 of them. We won most of the games.
When there is a subordinate clause or prepositional phrase, you almost always (but not quite always) need to use "most of the"
"Most of the dogs in this town are cute."
"I like most of the presents that my sister gave me."
*Adjectives usually (but not always) do NOT define a group with limited size, so don't use "of"
"Most small dogs are cute" NOT "most of the small dogs are cute."
Only say "most of the small dogs are cute" if you can point to a specific group of small dogs.
"This room is filled with dogs. Some of them are big, and some of them are small. Most of the small dogs are cute"
Finally, there are a few set phrases like "most of the time". Just memorize them.
The same rules work for "all" vs "all of" and "some" vs "some of"