Well, one place to start would be to consider how this poem presents its main theme, which is that of death. The poem features a narrator, who passes by a churchyard in the countryside and considers the meaning of the corpses buried in this churchyard. The graveyard seems to act as a reminder to the narrator of his own consciousness of mortality. Thus it is that the opening stanzas present a contrast between life and death. Thus it is that the "rude forefathers of the hamlet," "each in their own cell," are compared to various signs of the vigorous life of nature, such as "the moping owl," the swallow and the cock. You will also want to analyse the way that the poem begins by creating a mood enacting the theme of mortality. Consider the opening stanza:
The curfew tolls the knell of parting day,
The lowing herd winds slowly o'er the lea,
The ploughman homeward plods his weary way,
And leaves the world to darkness and to me.
Note how a depressing, serious and sombre mood is created through the reference to the gradual dimming of the light, the "weary" ploughman "plodding" and the cattle lowing. Symbolically, of course, the end of day could be said to represent the death of man, which makes the setting particularly fitting for the consideration of man's mortality that follows.
Hopefully this introduction will give you a basis on which you can base your further analysis of the poem, as the narrator discusses the dead in the graveyard and considers what he can learn from this visible sign of the impermanence of mankind.