"The Fly" begins with a cry of regret. The speaker, alarmed to discover that he's just accidentally swatted a fly, addresses it with remorseful affection, calling it "Little Fly" and observing that his "thoughtless hand" has brought an end to its "summer's play." His language makes it sound more as if he's killed a duckling than a fly.
Of course, it's pretty easy to kill a fly "thoughtless[ly]": such a small, fragile bug can be "brushed away" completely by accident—or by "thoughtless" reflex, for that matter, if it lands on one's face. The idea that it's the speaker's "thoughtless hand" that does the brushing here supports that reflexive reading; this swatting was an instinctive act of the speaker's body, not his conscious choice.
Most fly-swatting is so "thoughtless" that the swatter barely even registers what they've done. This speaker, however, is pausing to consider this everyday swatting more carefully. Addressing the fly directly, he treats it as a creature that was enjoying its "summer's play": in other words, as a conscious being that would probably have preferred to remain alive, just like the speaker himself.
In these first few lines, readers familiar with fly symbolism might get the sense that this will be a poem about how fragile and temporary life is. Flies traditionally symbolize death both because they're so easily squashed and because they tend to turn up where dead meat is available. But the speaker's response to the fly will go much deeper than a reflection on mortality. He's interested not just in the fact that he and the fly are both mortal, but that he and the fly are both conscious (or were, anyway). This will be a poem about the mysterious relationship between the mind and body.
That might come as a surprise to readers who glance at the poem's form. In a mere five quatrains of short, thumping dimeter lines (that is, lines with only two strong stresses apiece: "Little Fly"), there might not seem to be much room to explore consciousness itself. The singsong ABCB rhyme scheme similarly suggests nursery rhymes more than philosophy.
But as is so often the case in Blake's Songs of Innocence and of Experience, simplicity is deceptive.