“动词+one’s way to”是英语的惯用表达，意思是“以（动词所表示的意义）的方式”，sweat one’s way 意思是“以出汗的方式”，Sweat your way to good health 的字面意思是“以出汗的方式达到健康状态”，即锻炼好身体。更多类似例句如：

He groped my way to the door. 他摸索着找到了门。

He pushed her way to the front. 他挤到了前面。

I thumbed his way to Paris. 我搭便车去了巴黎。

I worked my way to the center of the crowd. 我费力地挤到人群的中心。

She ambitiously worked her way to the top. 她雄心勃勃地干到了高层。

She elbowed her way to the front of the queue. 她挤到了队伍的前面。

Steve fought his way to the front of the hall. 史蒂夫奋力挤到大厅的前面。