To do one's best to do something in Engpsh means to try as hard as possible to do it, or to put forth the maximum effort to achieve it. Some possible phrases to express this idea include:

give it one's best shot
try one's hardest
do one's utmost
put in one's best effort

For example:

"I know I'm not very good at math, but I'll give it my best shot and see if I can figure it out."

"I'm going to try my hardest to get this project done on time."

"I'll do my utmost to make sure everything is perfect for the party."

"I'm going to put in my best effort to win this race."