What rhetorical devices does Longfellow use in "A Psalm of Life"?

Rhetorical devices are persuasive devices.
In this poem, the speaker is trying to persuade us to lead active lives. He advises us not to think of life as a dream or to set our eyes on heaven and the afterlife. We should throw our energies into the here and now.
One way the speaker is persuasive is by using frequent exclamation points to emphasize his passion for living an active life. Through his emotional writing, he shows us he cares deeply about making an impact on this world. For example, he writes:

Life is real! Life is earnest!

He is not simply saying that—he is throwing all his intensity behind those ideas, almost shouting them.
The speaker also uses imagery to convince us of what he says. Imagery is describing using the five senses: sight, sound, touch, taste, and hearing. For example, he writes:

Be not like dumb, driven cattle!
Be a hero in the strife!

We can imagine being a head of cattle, slowly plodding along without purpose, or we can see ourselves as a hero gallantly fighting in the midst of battle. In putting these two images side by side, Longfellow creates an antithesis, which is the juxtaposition of two opposite ideas. Most of us would decide we want to be heroic warriors and take on life rather than be like cattle.

Longfellow also uses metaphor, which is comparison not using the words like or as, for example, when he writes that what we should leave behind us:
Footprints on the sands of time
He is comparing our achievements in life to footprints in the sand: most of us would want to leave behind some imprint of what we did in life after we die, so this metaphor might inspire us to action.