Use of "because of"

In high school, the teacher told me that because is used to answer “why” question, as below:

• Why you are you using my shoes?
• I am using your shoes because I like them.

However, the use of of after because looks like it changes the meaning to something completely different:

The sun hid its light because of the eclipse

How can I distinguish where I should use just a plain because without any of following it from where I should use the full because of phrase?

Because is a conjunction, and introduces a subordinate clause giving an explanation of what is expressed in the main clause. Because of means ‘by reason of, on account of’ and is followed by a noun phrase.

This is actually a point of grammar, not usage.

Because is a subordinating conjunction that can introduce an entire tensed subordinate clause (such clauses must contain at least a subject and a tensed verb). But it can also introduce just a noun phrase, instead of a whole clause.

When because introduces a noun phrase -- and not a clause -- the conjunction because adds the preposition of, to become the complex preposition because of. It's that simple.

• He left because we asked her to.
• He left because of our request.
• Because she intended to see us, she stayed until the end.
• Because of her intention, she stayed until the end.

Note that embedded questions and other types of clauses are considered noun phrases:

• He left because of what we said to her.
• He left because of her getting so upset.