What is the verb to make (someone) happy?
Is it "mutlu yapmak"?

Beni mutlu yaparsın - you make me happy

this could be:

"beni mutlu et!"

i think the verb is "mutlu etmek"

you make me happy=  beni mutlu ediyorsun

Yes..the verb is ´´mutlu etmek´´ =to make someone happy

there is another way of it which is ´´mutlu kılmak´´ but its not common ..

One of my dictionaries translates mutlu kilmak as exhilerate. Is that a good tranlation?

´´exhilarete´ means çok neşelendirmek (which is make someone very cheerfull´ so its not exactly giving the meaning of mutlu kılmak..

so ´´ mutlu kılmak ´´ is to make someone happy..let me give you an example;

Buraya gelmek beni her zaman mutlu kılıyor (kılar). (Coming here always make me happy)