The magnetic compass somehow makes use of Earth's magnetic field, much the way a standard compass does.

the way 后面是一个从句。the way 引导从句有两层含义：（1）as  （2）how

本句是 as 的意思，引导“方式从句”，是“比较从句”的一个子类，也可笼统分析为“比较从句”：

the way a standard compass does = as a standard compass does

much the way a standard compass does = much as a standard compass does

much 是程度副词，修饰引导从句的the way。字面上是加强语气，其实是削弱了从句的程度。—— “很像”，不是“真像”。

因此，句子结构是：

主句：The magnetic compass somehow makes use of Earth's magnetic field,

方式/比较状语从句：much the way a standard compass does.