Lines 1-6 Summary

Get out the microscope, because we’re going through this poem line-by-line.

My heart leaps up when I behold

Officially, this poem is untitled, and so this is just the first line of the poem, not the title. But it is important in setting up the rest of the poem.
Basically, the line shows us that the poem is going to be about something that makes the speaker's heart leap up, presumably from joy. It's common to say "my heart leapt," but think about this expression. The heart has no legs. This makes it hard for it to literally leap on its own, so this is an example of personification. We can infer that the heart will "leap," even if the speaker is otherwise depressed. Perhaps he actually feels a kind of jolt in his chest.
We won't know why the speaker's heart is leaping up until we get to the next line. The suspense is killing us! For now, though, this line break helps with the rhythm of the poem and keeps us readers on our toes (for more on rhythm, go check out "Form and Meter").
Keep in mind that "behold" means to see or observe something, not to hold it. Behold is a pretty majestic word, so we suspect we're being set up for a majestic sight…

A rainbow in the sky:

We find out what makes the speaker's heart leap up: a rainbow. Because of the strategic line break, and the indentation, our hearts leap a little bit when we read this line too—or at least our eyes do.
When you read this line, picture the last time you saw a rainbow and think about how it made you feel. Was it like this guy?
Note that the line ends with a colon. This means that what follows is probably related to it. Let's check it out…

So was it when my life began;

This line and the next few after it create a sense of time in the poem. Here we learn that the speaker has had this feeling about rainbows ever since his life began, which we take to mean his childhood, when he was just a wee tyke.

So is it now I am a man;

This line continues the thought from the line before. Now we learn that the speaker still gets excited by the sight of a rainbow, even as a mature adult. We understand that the speaker is reflecting as an adult, but really, he's just a kid at heart.

So be it when I shall grow old,
Or let me die!

So we've heard about the thrill of rainbows in the speaker's past and present. Now we hear about the future. The speaker is sure that when he grows old, he will still be thrilled at the sight of a rainbow.
Then we get an indented line again, and we encounter a bit of a pause, at least visually. At the end of this pause, the speaker lets us know that he is so thrilled by rainbows that, if he ever lost this thrill, he would want to die. Intense.
Whom is he talking to here, though, when he says "let me die"? God? The Grim Reaper? Whomever he's addressing, they're not around in the poem. This kind of address to an absent or abstract audience is what's called in the biz an apostrophe.
This line is even followed by an exclamation point, so the speaker clearly wants to emphasize it! For him, life without the capacity to appreciate nature's beauty would not be worth living.