* Form : verb stem + -기
ex) 하|다 (to do) --> 하 + 기 --> 하기 (doing)
먹|다 (to eat) --> 먹 + 기 --> 먹기 (eating)
놀|다 (to play) --> 놀 + 기 --> 놀기 (playing)
As you might notice, when you add -기 to the verb stem, it changes verbs to nouns. So it is like gerund in English.
* 내(my) 취미는 (hobby) 야구하기예요. (is playing baseball)
* More sample sentences
e.g. 한국어 배우기가 어렵지 않아요. (Learning Korean is not difficult.)
e.g. 제 새해 결심은 '운동 열심히 하기'예요. (My new year's resolution is exercising hard.)
Hope it helps!