The machine-gunners took turns firing from the trenches.

machine-gunners 是由 machine gun（机枪）加后缀 -er（表示从事某种职业的人）构成的复合名词，指"操作机枪的人"，即"机枪手"。 took turns 是动词短语 take turns 的过去式，take turns 意思是"轮流做某事"。