To parse a conjunction or connective:

Tell the conjunctions part of speech, and why.
Tell the class to which it belongs.
Tell what elements it connects.

Parse the conjunctions in the following sentence:

Socrates and Plato were distinguished philosophers.

And is a conjunction.
It is used to connect sentences or the parts of sentences.
It is a coordinate conjunction that connects similar elements.
It connects Socrates and Plato.

Parse the conjunctions in the following sentence:

Wisdom is better than riches.

Than is a conjunction.
It is a subordinate conjunction that connects dissimilar elements.
It connects the proposition than riches with better.

Parse the conjunctions in the following sentence:

We must either obey or be punished.

Either is an alternative coordinate conjunction.
It is used to awaken expectation of an additional idea, and also to introduce that idea with emphasis.
Or is an alternative coordinate conjunction and with its correlative either it is used to connect the predicate must be punished
with must obey.

Parse the conjunctions in the following sentence:

Though he slay me, yet will I trust in him.

Though is an adversative subordinate conjunction.
It is used to awaken expectation of an additional idea.
Yet is an adversative subordinate conjunction.
With its correlative though it connects the subordinate clause he slay me, with the principal clause
will I trust in him.