I would say that the poet's tone is accepting and even reflective. The poet is glad he lived, but he's ready to die. He's rather philosophical about his death. Dying isn't a morbid subject for him, and he voices no fear of it. He readily asks for a grave to be dug for him, and he assures his listener that he already has a will written out. In other words, he's put his house in order, and he's ready to leave the world of the living.
The main themes of this poem are the inevitability of death and death as a respite at the end of an eventful life. In the poem, the poet calls the grave a "home" for seafaring sailor and roaming hunter alike. The last lines of the poem imply that the grave willingly accepts all who choose to lie in it.
The poet uses alliteration (starry sky) to make a strange request: he wants his grave to be dug under the night sky. He doesn't say why; perhaps he feels that his request is appropriate because he will soon be enveloped in darkness in the grave.
In the poem, the rhyme scheme is aaab cccb; the poem is written in two quatrains.
Under/ the wide/ and star/ry sky/
Dig the/ grave and/ let me/ lie:
Glad did/ I live/ and glad/ly die,
And I laid/ me down with/ a will.
The above is the first stanza, and it is an interesting one. We have four poetic feet in the first three lines, so this would make the lines tetrameters. The last line has three feet, so this would make it a trimeter. The tetrameters appear to be a mixture of trochaic (accented followed with unaccented words) and iambic (unaccented followed with accented words). Meanwhile, the trimeter or last line can be said to be anapestic (unaccented/unaccented/accented) with iambic (unaccented/accented) thrown in towards the end. The second stanza is similarly structured.
In the last stanza, the poet uses repetition (through the word "home") to reinforce the idea of the grave as his final resting place.
In this poem, the "wide and starry sky" imagery alerts us to a sense of freedom and space. The poet wants to be buried under this wide expanse; under the sky, his grave will be his "home." He will be free from all responsibilities and earthly burdens.
As mentioned, the poem consists of two quatrains. It is rustic in style. In the last stanza, the poet characterizes himself as a sailor "home from the sea" and a hunter "home from the hill." He has traveled far and worked hard; it is time for the last stage of his life: death. To understand all that style encompasses in poetry, please refer to The Meaning of Style in Poetry.