For example, I know that if I wanted to say “Most of the people here are good.” I know I should say something like:
Die meisten Leute hier sind gut.
Is that true in all situations in which I have to use the most? For example, if I wanted to say “Most of the schools don’t teach German”, would that be the same as above?
In your heading you ask for »the most ...«, but in the body of your question you ask for »most of ...«. My English is not the best, but I'm pretty sure, that those phrases are different in English. So why do you think they should be the same in German?
Peter is the most intelligent person I know.
Peter ist der intelligenteste Mensch den ich kenne.Daylight is the most pleasant light.
Tageslicht ist das angenehmste Licht.
In this examples you use »the most« to build the superlative of an adjective. In German there is no superlative-construction that uses »am meisten« or something similar. So this are wrong sentences:
WRONG: Peter ist der am meisten intelligente Mensch den ich kenne.
WRONG: Tageslicht ist das am meisten angenehme Licht.
Most of the people living there use to eat pork.
Die meisten Leute die dort leben essen Schweinefleisch.Many companies provide extra benefits for most of their employees.
Viele Gesellschaften bieten den meisten ihrer Mtarbeiter zusätzliche Vorteile.
Here you use »most of« to tell, that almost all (but still less than 100%) members of a set have a certain property. As you can see, the German construction for this is very similar to the English.
The patterns are (same indices mark same parts of speech):
If you use it together with an article:
Eng: {most of}1 <article>2 <noun>3
He no longer trusts {most of}1 the2 banks3.
Ger: <Artikel>2 meisten1 <Substantiv>3.
Er vertraut den2 meisten1 Banken3 nicht mehr.
If you use it together with a pronoun:
Eng: (<article>0) {most of}1 <pronoun>2 <noun>3
She hasn't seen (the0) {most of}1 her2 students3 for years.
Ger: <Artikel>0 meisten1 <Pronomen>2 <Substantiv>3.
Sie hat die0 meisten1 ihrer2 Schüler3 seit Jahren nicht gesehen.
In this example you can omit the article before »most of« in English (that's why I put it in brackets), but you have to use it in German.
But there are also exceptions:
My cat sleeps most of the time.
Meine Katze schläft meistens.Walter, Maria and most of all Peter need to clean their shoes before they enter the house.
Walter, Maria und vor allem Peter müssen sich die Schuhe putzen bevor sie das Haus betreten.
Yes, "Most of.." means "Die meisten...".
It's as easy as you think :)