First, in order to give some boundaries to this answer, let me assume that the questioner knows something about the Romantic Poetry movement, the Lake District poets (Wordsworth, Coleridge, Byron, Burns, etc.), and the definition of an ode.
In a poem of this length, the first step toward understanding how the symbolism works is to find three or four major symbol clusters that gives the poem some structure. Here, the first step is to note that the narrator (poet) in real life hears a skylark’s song, which sets off his poetic sensibilities. Next, we note the narrator’s immediate reaction, captured in such phrases as “blithe spirit,” “unpremeditated art” – that is, the bird is compared to an unearthly, heaven-connected event, not merely a physical bird. By addressing the bird, the narrator is able to describe his sight of the bird as well (at first he simply hears it, then spots it as it flies into “the blue deep.”) He continues to describe the sky (“golden light’ning,” etc.) and strengthens his second observation – that the bird is free and unfettered, “unbodied” and inspiring. As the flight continues, the song remains. By adding metaphors to describe the day’s light (arrows of the sun, etc.), the poet announces his departure from realistic description, preparing to begin the part of the ode (“What is most like thee?”) that deals with comparisons of the bird’s song and flight to the poet’s human experiences, such as “Singing hymns (ie., writing poems) unbidden.” This set of symbols (to “thy music doth surpass.") leads us into the section about what we might learn from the skylark, and speculation of what inspired the bird’s song. The last stanza expresses the poet’s wish that he might write poetry as effective, as harmonious yet mad (ie., not bound by human logic or sense), as the bird’s song.
This admittedly skeletal breakdown shows how the symbolism works to our conclusion: the skylark’s song is an inspiration to the hearer to write poetry with the same properties – heavenly, harmonious, worth listening to.