How did humanism influence Shakespeare?

In Hamlet, Shakespeare articulates through Hamlet the humanist worldview in a nutshell:

What a piece of work is a man! How noble in reason, how infinite in faculty! In form and moving how express and admirable! In action how like an angel, in apprehension how like a god! The beauty of the world. The paragon of animals.

Miranda in The Tempest likewise exalts humankind when, on first seeing a group of adult men, she exclaims:

O brave new world that has such people in it

Humanists, such as Pico della Mirandola in his Oration on the Dignity of Man, led the way for playwrights like Shakespeare by putting humans in a central position as the glory of God's creation.
This emphasis on the positive attributes of human beings rather than on humans as miserable sinners influenced Shakespeare to celebrate his human characters. One way he does this is to develop them beyond being the mere "types" of Medieval drama. There, a one-dimensional human character would represent a single vice or attribute, such as envy or patience. Shakespeare, in contrast, did his best to capture the full dimensionality of people.
Hamlet, for instance, is called the first modern hero because Shakespeare focuses so much attention on his interiority: on what he is thinking and feeling. Many other characters also benefit from this nuanced, in-depth treatment. Shylock is not simply a stereotype of a legalistic Jew, but he is also a caring father and a once loving husband, as well as man who is presented as cruelly denigrated for his faith. Falstaff is both a cheerful party animal and an unabashed coward. An emphasis on the importance of humanity allowed Shakespeare to explore people as they truly were—and are—rather than as cardboard figures in a morality play.
Further, humanism brought Greek and Roman literature to the forefront of European learning. This influenced Shakespeare to adapt classical works, such as those by Ovid, into Renaissance plays. For that reason, we have such dramas as Romeo and Juliet, which have enriched the English literary canon.