The poem opens by giving its addressee various instructions about things not to do. And, right of the bat, the speaker is emphatic—repeating "no" twice (technically something called epizeuxis) followed by "go not," just in case the listener isn't sure how serious the speaker takes this!
It's worth noting early on that the addressee of the poem is never made clear. The poem originally had another stanza at the start, which focused on a hero-figure questing to find the goddess Melancholy—this may explain the starting point for this instructive tone. But, of course, that stanza was deleted, so the poem could be interpreted as addressed to some unknown recipient, to the reader, to anyone who has ever experienced melancholy—or to some combination of all of these.
The poem's first instruction, then, is that this melancholic person should not go "to Lethe." This is an allusion to a river in the mythological Greek underworld. According to myth, drinking from this river will cause someone to forget everything and enter a kind of state of oblivion. The speaker, then, is cautioning against reckless, self-destructive oblivion. Though the point is not made till later in the stanza, this is because the speaker views the melancholic state—the "wakeful anguish of the soul"—as something to be embraced, rather than drunk or drugged away.
The next warnings are against "wolfsbane," "nightshade," and the "ruby grape of Proserpine." The first of these is a poisonous flower, also known as monkshood. The caesuras surrounding the clause "tight-rooted" in line 2 conveys the way the plant is tightly embedded in the ground, meaning anyone who wants to take it out needs to be pretty desperate and determined. The consonance of /t/ sounds in the phrase also sound tight and compressed.
Nightshade is another deadly plant (also know as atropa belladonna), while the "ruby grape of Proserpine" is another classical allusion. Proserpine, or Proserpina, is the Roman myth equivalent of the Greek Persephone. Long story short, Persephone is the daughter of Zeus and a goddess named Demeter. Hades, ruler of the underworld, kidnaps Persephone and makes her his queen. Her return to earth each year marks springtime; she is associated with both death and vegetation.
What's important here is that all of the above can be grouped together as intoxicants, and they also hint at the act of suicide. They are, then, part of the speaker's way of building an argument not quite in favor of—but against the rejection of—the melancholic state. That is, the speaker is telling the listener not to actively try to dull the pain of melancholy.
"Yew-berries," mentioned in line 5, are also highly toxic. To make a rosary of them would be to somehow construct a personal religion or way of life around intoxication, as though they are an object to aid prayer. Of course, the speaker rejects this idea too.