Formal:
* Illuminate: To shed light on, making something clear or understandable.
* Elucidate: To explain in detail, making something clear and easy to understand.
* Explicate: To explain the meaning of something.
* Clarify: To make something easier to understand by removing confusion.
* Inform: To provide knowledge or information.
* Educate: To teach someone something, often formally.
* Instruct: To teach someone how to do something.
Informal:
* Shine a light on: To bring attention to something.
* Open someone's eyes: To make someone aware of something they didn't know before.
* Give someone the lowdown: To provide someone with all the information they need to know.
* Fill someone in: To provide someone with information.
* Put someone in the picture: To make someone aware of what is happening.
* Show someone the ropes: To teach someone the basics of something.
The best synonym to use will depend on the specific situation and the desired tone.