Jisho

It's used when you are asking someone to do something.

くれ/ください = please
くれた/くださった = did it for me

教えてくれ/教えてください = please teach (me)
教えてくれた/教えてくださった = (he) taught (me)

生きる意味を教えてくれ = please teach me the meaning of life.

あげる has a similar meaning. It's used when you are doing something for someone.

生きる意味を教えてあげる = I'll teach you the meaning of life.

もらう can be used like くれ too but I'm not sure on the specifics.

Also beware that くれる is also a verb meaning to give.

金はくれない = will not give money.

すごい。
Thanks that was super specific, I love it!

くれる is specifically "to give to me"; you can't use くれる if you're giving something to another person. So, 金をくれない is "will not give money to me". There's a bit more to it than that since you can also use it to refer to something being given someone who's in your in-group (e.g. family), but that's the general gist.

もらう is "to receive". The main difference between くれる and もらう is the subject of the verb. If A gives B a cookie, you could either say "ＡさんはＢさんにクッキーをあげました" or "ＢさんはＡさんにクッキーをもらいました". Note that A and B are in grammatically opposite positions for each verb.

～てくれる and ～てもらう are very similar, but to put it simply, ～てもらう is like "I got [person] to do [thing] for me", whereas ～てくれる is just "[Person] did [thing] for me." Getting someone to do something for you sounds manipulative in English, but in Japanese, ～てもらう sort of expresses gratitude that they did the thing for you. Example: 父に車を買ってもらいました.

Also, about くれる vs. くださる: with the exception of ～てください, くださる is a very formal word (it's the 敬語 form of くれる) and therefore should only be used in formal situations. You're much more likely to use 教えてくれた than 教えてくださった.

Hope that helps!