There doesn't seem to be a set phrase that matches "trying to" exactly.
There are a few different ones depending on the situation.
The key is the verb 하다, which means "do" or "perform", but has many extended uses as well.
하다: 일을 하다 = Do the work; 운동을 하다 = Work out (one's body) - original meaning
하다 (extended meaning): make an effort; intend to...
-려고: verb conjugation for "to do (something)"; with the intention of...
ex) 가려고: 가다(go) + 려고 -> 가려고: to go
-려고 하다: make an effort to ..; try to ..
So the basis for "trying to" is usually "-려(고) 하다" or just "-려 하다" (shortened form).
In real life, there are more than way of saying "trying to":
* I'm trying to read.
1) (나는) 책을 보려(고) 하고 있어: (a little long and formal)
2) (나) 책 좀 보려 해: 좀 means "a bit", so "I'm trying to read a bit".
3) (sk) 책 좀 보는 중이야 I am reading (a bit). 중이야: I am ...ing.
* I'm trying to get it done.
1) (난) 이 일을 마치려 하고 있어
2) (난) 이 일을 마치려(고) (해): With "해" omitted it is still clear and natural
3) (난) 이 일을 마치려고 하는 중이야
4) (난) 이 일을 마치려는 중이야
* I'm trying to finish my homework.
1) (난) 숙제 끝내려(고) 해 (끝내다 = finish)
2) (난) 숙제 좀 끝내려고 ...
3) (난) 숙제 좀 끝내려고 하는 중이야
4) (난) 숙제 좀 끝내려는 중이야
So -려 하다 is the best way, but in casual situations, -는 중이야 (am ..-ing) is also used often.