Ok.  Essentially, all components "do something" in normal
operation. (There can be some components that "do something"
only in abnormal conditions.)  Lashing a bunch of components
together in a particular way makes them "do something"
as a group.  Perhaps they make an oscillator, or an amplifier,
or a regulator or a filter - whatever. Call that group a circuit,
and identify it by its function - eg "an amplifier circuit", "a
voltage regulator circuit" etc. You need to learn what each
component does. You need to learn what each circuit does.
Each circuit can be thought of as having input(s) and output(s)
and some circuits also need a power source.

Once you have an understanding of basic circuits, troubleshooting
consists of determining whether the input(s) is(are) correct and
whether the output(s) is(are) correct.  When you find a circuit
that has correct input, but has incorrect output, you know
that either that circuit is bad, or the output is being improperly
influenced by the next circuit in line.  To do this, you need
to know what a proper input is, and what a proper output is.
Once you know what input and output to expect, you can anwser
your own question about using a DMM to troubleshoot.  This
assumes that you already know what your DMM is capable of.