kanrinin ni gomi no dasikata wo kiitara, totemo teinei ni osiete kuremasita.

Because 管理人に marks the person the speaker asked.

With 聞く, a common pattern is:

• 人に ものを 聞く = ask a person about something

So here:

• 管理人に = to the building manager / apartment manager
• ごみの出し方を = about how to put out the garbage

The whole first part means when I asked the manager about how to put out the garbage.

管理人 usually means a manager/caretaker/superintendent of a building, apartment complex, dorm, etc.

In this sentence, it most likely means someone like:

• an apartment building manager
• a caretaker
• a superintendent

So this is probably a situation where the speaker asked the person in charge of the building about the garbage rules.

ごみの出し方 means how to put out the garbage or the way to dispose of trash.

It breaks down like this:

• ごみ = garbage, trash
• 出し方 = way of putting out / way of doing

So ごみの出し方 is literally:

• the way of taking out/putting out garbage

In Japanese, X の Y often works like Y of X or X-related Y, so this phrase means the method for dealing with garbage.

出し方 is made from:

• 出す = to put out, take out
• the stem 出し
• 方（かた） = way of doing something

So:

• 出す → 出し方 = way of putting out

This pattern is very common:

• 食べ方 = how to eat
• 使い方 = how to use
• 書き方 = how to write

So ごみの出し方 is a very natural expression for how to take out the trash.

Yes. In garbage-related contexts, 出す is often used for putting garbage out for collection.

Literally, 出す is a broad verb meaning things like:

• take out
• put out
• send out
• submit

With garbage, it usually refers to putting it out in the proper place/time, not just physically removing it from your room.

So ごみを出す often means:

• put the trash out
• take the garbage out for collection

Here, 聞いたら means something like when I asked or after I asked.

The form 〜たら can mean:

• if
• when
• after doing

In this sentence, because the main clause is a past event (教えてくれました), the natural meaning is:

• When I asked the manager..., he/she explained it very politely.

So this is not really a hypothetical if. It is describing what happened after the speaker asked.

This is very normal in Japanese.

In subordinate clauses like 〜たら, Japanese usually uses the plain form, even in polite speech.

So:

• 聞いたら = plain form inside the clause
• 教えてくれました = polite ending for the whole sentence

This mix is standard Japanese. The politeness of the sentence is mainly shown at the end.

Because 丁寧 is describing how the manager explained, so it needs the adverbial form.

• 丁寧 is a na-adjective
• to use it adverbially, you add に

So:

• 丁寧な人 = a polite/courteous person
• 丁寧に教える = explain politely / explain carefully

Here, とても丁寧に教えてくれました means:

• explained it very politely/carefully

くれました adds the idea that the action was done for the speaker's benefit.

Compare:

• 教えました = taught / explained
• 教えてくれました = kindly taught/explained to me (or to someone close to me)

So 〜てくれる often shows that someone did something for the speaker, and it can carry a sense of appreciation.

In this sentence, it makes the meaning feel more like:

• The manager kindly explained it to me.

That fits very naturally with とても丁寧に.

The subject is omitted, which is very common in Japanese.

From context, we understand:

• the speaker asked the manager
• the manager explained it to the speaker

So the implied meaning is:

• When I asked the manager how to put out the garbage, he/she explained it to me very politely.

Japanese often leaves out subjects and objects when they are obvious from context.

Yes, it is omitted because it is already clear from the first half.

In the first clause, the speaker asks about:

• ごみの出し方 = how to put out the garbage

In the second clause, Japanese does not repeat it, but the understood meaning is:

• the manager explained how to put out the garbage

So the full idea is:

• When I asked the manager about how to put out the garbage, he/she explained it very politely to me.

Yes, and the meaning would be similar, but the perspective changes.

• 管理人が（私に）教えてくれました
  = The manager explained it to me.

• 私は管理人に教えてもらいました
  = I received an explanation from the manager.

Both can express gratitude or benefit, but:

• くれる focuses more on what the other person did for me
• もらう focuses more on me receiving the favor

So 教えてくれました is very natural here because the sentence is describing the manager's helpful action.

Usually 管理人に聞いたら is better here, because the speaker is actively asking the manager.

• 人に聞く = ask someone
• 人から聞く = hear/learn from someone

So:

• 管理人に聞いたら = when I asked the manager
• 管理人から聞いたら would sound more like when I heard from the manager, which is a different nuance

For this sentence, に is the natural choice.