No, no, go not to Lethe (1)
"Lethe" is the river of forgetfulness in ancient Greek mythology. Abusing alcohol is sometimes described metaphorically as plunging into the river Lethe, since booze can make you forget your troubles. But that's just what this poem is advising against—we should embrace our melancholy and face it while we're alert and aware.
[…] neither twist Wolf's-bane, tight-rooted, for its poisonous wine; (1-2)
There are a lot of possible meanings twisted up in these lines. The most obvious meaning is that we shouldn't commit suicide by drinking poisonous wolf's-bane to avoid our troubles. But since wolf's-bane is actually medicinal in very tiny doses, the speaker could also be telling us not to take any kind of drug to deal with the pain of melancholy. And by describing it as a "poisonous wine," he may also be advising against the abuse of alcohol to deal with depression.
Nor suffer thy pale forehead to be kiss'd By nightshade, ruby grape of Proserpine; (3-4)
Again, the speaker tells us to reject suicide as an option. And by rejecting the "ruby grape" that is used to make wine, he again implies that we should reject the abuse of alcohol, as well.