We say "at the end (of something)" to say "at the time when something comes to an end": at the end of the week, at the end of the book, etc.

Example:

I'm leaving for Moscow [ ] the end of the week.

The opposite of "at the end of" is "at the beginning of".

We say "in the end" when we mean "finally".

Example:

I didn't know what to say. [ ] the end I just told them the truth.

The opposite of "in the end" is "at first".

We say "by…" to explain how we do something: by cheque, by credit card, by post.

Example: I'll pay [ ] credit card.

If we use money in form of notes and coins to pay, we say "in cash".

Example: I didn't have my credit card. I paid [ ] cash.

We say "by…" to explain how we travel: by bus, by plane, etc.

But if we use "a/the/my + noun", we use "on/in": in my car, on the plane.

Example: We went to India [ ] plane.

We came here [ ] my car.

If we walk, we say "on foot".

Example: I don't want to go by car. Let's go [ ] foot.

We say "excited/nervous/worried/ upset/happy/angry/annoyed + about something".

Example: I'm nervous [ ] my exams.

We say "patient/angry/annoyed/furious + with somebody".

Example: She's so patient [ ] children. She'll make a good teacher.