Alliteration is a consistent presence in "Ode to a Nightingale" (which is also full of consonance and assonance). This is a very beautiful sounding poem, which is part of the point; the speaker is trying, in part, to use poetry to achieve the same kind of beauty embodied by the nightingale's song.
Alliteration also reflects the lines' content in certain points. In lines 1 to 3, for example, note the many /d/ sounds. This is a heavy, voiced consonant that adds a sense of weight and insisting thudding to these lines—which is appropriate, given that the speaker is talking about being very down:
My heart aches, and a drowsy numbness pains
My sense, as though of hemlock I had drunk,
Or emptied some dull opiate to the drains
The /d/ sound returns in line 12: "deep-delved" supports the image of "vintage" wine cooled in the belly of the earth. The two /d/ sounds are again quite strong, as though being dug into the line themselves.
Later in the first stanza, the alliteration of "singest" and "summer" suggests the first notes of a tune (as though the poem is going to play the /s/ song!). In doing so, alliteration evokes the sound of the nightingale itself. The /s/ sound is again associated with beauty and comfort via the alliteration (and broader consonance) in stanza 2:
Dance, and Provençal song, and sunburnt mirth!
O for a beaker full of the warm South,
The /s/ sound is connected to the bird throughout the poem, in fact. For instance, in line 59, the two /s/ sounds of "still" and "sing" echo the first mention of the nightingale's song in the first stanza (again, "singest" and "summer"). And in line 65, the alliteration suggests the continuity of the nightingale through the ages, from Biblical times all the way to the poem's present. The uniformity of /s/ sounds in "self-same song" suggests a tune that has gone unchanged over centuries, perhaps even millennia.
Line 15 also introduces alliteration start on the bright /b/ sound:
O for a beaker full of the warm South,
Full of the true, the blushful Hippocrene,
With beaded bubbles winking at the brim,
The /b/ sound rings out across these lines, adding a burst of brightness to this description. In line 17 the alliteration (and consonance) is almost onomatopoeic with the phrase "beaded bubbles." Try reading these lines out loud to notice how the /b/ cause the mouth to make a bubble-blowing action!
Another striking example stretches across the end of the second stanza and into the start of the third:
And with thee fade away into the forest dim:
Fade far away, dissolve, and quite forget
These /f/ sounds link three key components of the poem: the act of forgetting, the forest in which the speaker stands, and literal and metaphorical distance. The speaker can hear the distant sound of the nightingale among the trees, and longs to "fade" away from the human world, to "forget" the suffering and pain of human consciousness. This /f/ is a soft sound too, representing the way that "fad[ing]" is a gradual process.
The final key example is near the end of the poem. In line 70 "Faery" chimes with "forlorn" (and the latter word is then repeated at the start of line 71). This echoes the earlier association of /f/ with "fading," but also links the idea of being "forlorn"—sad and melancholy—with fantasy. If the "faery lands" are tied to the human imagination, which the speaker names with another /f/ word, "fancy," then it is in part this ability to deceive themselves that makes people "forlorn."