When is it appropriate to use "Yeah" and "Yep" as variants of the word "Yes"?

As a learner of English I know that yes is a standard variant and the other two are informal, spoken words. I know nothing more about it, and always try using the yes variant, just to not sound inappropriate. But I'd like to be able to not sound too formal in a casual conversation.

Could you help me understand the differences between these words and the contexts in which it is okay to use them?

You are correct that "yeah" and "yep" are informal variants of "yes." In conversation among friends, any form is appropriate, but "yep" has a slightly dismissive tone.

"Did you find your wallet?"

"Yeah, I left it in the other room."

As opposed to

"Did you get directions to the theater?"

"Yep."

In the second example, you're implying that you've already got directions and you don't need to spend time hearing them again.

I use yeah or yep/yup when speaking casually. I tend to use yep/yup when it is being spoken by itself. I also would correspondingly use nope in the same way.

Did you do it?

Yeah, I did it

Yep.

Yes is not a formal word; you can use it in both formal and informal contexts.

Looking at the definitions given for yeah, yeh, yep, or yup, all those words are defined as exclamation & noun nonstandard spelling of yes, representing informal pronunciation.
Looking at the examples provided from the Werriam-Webster Online, it seems that yeah, and yep are used in two different cases. Yep is used when it's the only word in the answer; yeah is used in the other cases.

That's really what she said?
Yep.

That looks good.
Yeah, I think so too.

Yeah can also be used in a partial negation [yeah, but] meaning that you are affirming only a portion of the question.

Friend: Did you get movie tickets for me with the money I gave you?

You: Yeah, but they cost ten dollars more than you gave me for them. Would you be willing to pay for the popcorn?

Friend: Yep.

You: OK. See you there.