try (one's) hand (at something)
To attempt to do something new; to try something for the first time. I need a new hobby. Maybe I'll try my hand at painting! Thanks for letting Janet come to rugby practice with you. I know she's eager to try her hand.
try one's hand (at something)
to take a try at something. Someday I'd like to try my hand at flying a plane. Give me a chance. Let me try my hand!
try (one's) hand
To attempt to do something for the first time: I tried my hand at skiing.