From childhood's hour I have not been As others were; I have not seen As others saw (1-3)
The speaker has marched to the beat of his own drummer for a long time—since he was a child, in fact. There are all the "others," and there is him. The repetition of "I" in these lines will continue throughout the poem, and emphasizes the speaker's singularity.
I could not bring My passions from a common spring (3-4)
The distinction between the speaker and everybody else is further described. His passions do not come from a "common spring." In a way, then, the speaker becomes associated with what is uncommon. This foreshadows the sense of uniqueness we detect later in the poem.
From the same source I have not taken
My sorrow (5-6)
This marks the third time the speaker has said "I have not." All these negatives ("have not") make us think that being different is a lot like, well, not having something—like friends, or things in common with other people. It sounds like poverty to us. Bad times.
I could not awaken My heart to joy at the same tone; (6-7)
That phrase "could not awaken" is really troublesome. For a brief second, we think the speaker is either dead or permanently asleep because the line ends—yikes. This suggests that isolation is eerily similar to death, or being really, really, sleepy.
And all I loved, I loved alone (9)
Major alliteration going on here, that's for sure. And of course, this is the central moment of the poem, where "alone" is redefined. It's not just a case of "Oh, I'm all alone and in love by myself." It's also "I alone am the only one who loves." So, at least the speaker has that going for him.
And the cloud that took the form (When the rest of Heaven was blue) Of a demon in my view. (20-22)
A cloud that takes the form of a demon? This is classic Poe. It's also a sign of how the speaker's isolation has affected him. Part of the reason, perhaps, that the cloud takes the form of the demon is because the speaker is already feeling pretty bummed about everything.