Usually Korean doesn't have words for "let", and "make" as in "let me do it" and "make me do it"
So instead, the language uses grammar to express that. The grammar used for "make" and "let" is the same. (If you think about it, the meanings in English are quite similar)
The grammar is (verb)하게 하다~
Make (someone) do it - 하게하다
Make someone go- 가게하다
Make someone drink 마시게 하다
Make someone leave 나가게 하다
So you can see that you take the verb stem, drop the 다 and add 게, then add the verb 하다, and you got it.
1. That makes me sad
나를 슬프게 한다.
2. What you say makes me happy
네가 나한테 해주는말이 나를 기쁘게한다
3. That person makes me angry
쟤가 (or) 저사람이 나를 화나게한다
4. Too much food makes you fat
(this one, you don't need to use the grammar for "make"
너무 많이 먹으면 뚱뚱해진다
This one is just simply "if you eat a lot you get fat". You COULD go out of your way to say "makes me fat", but Koreans don't really use that grammar for this kind of sentence.
So keep that in mind when studying Korean. English speakers like to use words like "make" and "let" , and it CAN be translated, but you will find it shows up less in conversation among Koreans than it would among English speakers. That being said, the grammar is still very useful.
As for "let", you would see this grammar less, and instead you would just see "gave me permission to"
So sentences where in English you would say "let", in Korean you would see sentences that emphasized "permission" (허락) , "give permission" (허락 해주다)
So you can say "그사탕을 먹는걸 허락 해주줬다"
Maybe this is something you would say if your Dad let you eat candy.
Otherwise, there are sentences like this. This sentence uses "send someone out" (which could be translated as "let someone go out"
>>선생님이 보내주셨다 -
"The teacher let me leave" (literally: The teacher sent me out)
Notice the subject is not always clear in the sentences above, as leaving out the subject is quite common when it's implied who you are talking about. You can always add the subject to emphasize, or when it is not clear who it is.
Note: If a Korean native speaker notices a mistake and wants to correct my answer, feel free!!
Or add anything if you feel like it clarifies the grammar.
There are always different ways to approach grammar. I hope my answer helps! ^_^