At one point early in Act 5, scene 2, Hamlet actually uses the word "learning" when describing the usefulness of having very clear handwriting. Here is what he says (speaking to Horatio):
I once did hold it, as our statists do,
A baseness to write fair, and labour'd much
How to forget that learning; but, sir, now
It did me yeoman's service.
In other words, he once considered it petty to write clearly and therefore actually made an effort to make his writing unclear, even though he had learned earlier to write clearly. However, he recently found it helpful (in disposing of Rosencrantz and Guildenstern) to write very legibly.
This is a trivial reference to learning, but it seems to be the only time in the play when the word "learning" is actually used.
Hamlet shows a more serious interest in learning when instructing the players about proper ways of acting.