Translations of "to try"
A simple form of try is 试一试： ‘试一试某事’ = 'give something a whirl/shot'
I often hear:
我不会！ I can't do it!
试一试！ Try!

You can often replace 试一试 with 尝试。

You can also use 试： 我可以试一下这双鞋吗？

try hard (to do sth.) is 努力： 如果你努力就能够做到。

also 尽力： try your hardest (to do sth.): 我们会尽力完成。