"To do one's best" 和 "to give it one's all" 是用英语表达“尽力做某事”的两种说法。
"To do one's best" 是指尽可能地做到最好，是一个常用的习语。例如：
I will do my best to finish the project on time. (我会尽力完成这个项目）
He always does his best in everything he does. (他总是尽力做到最好)
"To give it one's all" 是指全力以赴，是一个比较俚语的表达方式。例如：
She gave it her all in the marathon, but unfortunately didn't win. (她在马拉松比赛中全力以赴，但不幸没有赢)
He always gives it his all, no matter what the task is. (无论任务是什么，他总是全力以赴)