I am reading a book where I came across a line that says
"I made do with coffee and a sandwich for breakfast and dozed for an hour"

How common is it for people to use "made do..." expression. It sounds a bit peculiar to me.

See a translation

It is no longer commonly used in that context, however it is still commonly used in more serious contexts.

Examples:

We lost the finished presentation, but we we made do with the samples and preparation notes.

“We had very little money growing up, but my parent always made do.”
(Found ways to still provide them what they needed)

A: I’m sorry for your loss.
B: Thank you, I relied on him/her so much, my life is going to change a lot.
A: Are you going to be okay?
B: I don’t know, but I’ll make do.
(Unknown emotional result, but surviving and still doing what needs to be done)