How does the phrase “long I stood” (line 3) characterize the speaker’s deliberations when choosing which road to take?

First, it's clear that the line "long I stood" suggests that the poet thought carefully about his decision. Let's examine it in more detail. The first stanza of the poem poses a problem:

Two roads diverged in a yellow wood,And sorry I could not travel both And be one traveler, long I stoodAnd looked down one as far as I couldTo where it bent in the undergrowth;

The problem is, of course, ...

First, it's clear that the line "long I stood" suggests that the poet thought carefully about his decision. Let's examine it in more detail. The first stanza of the poem poses a problem:

Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

The problem is, of course, which road to take? But this is not a problem of finding his way, exactly; presented with two routes, equally beautiful, which offers the greater pleasure? The poet is "sorry I could not travel both / And be one traveller"—that is, he is sorry he cannot somehow split himself into two and travel both roads simultaneously. There is only one of him. He has to choose.

Part of the power of the poem is its immediacy. The reader can easily visualize the "yellow wood" and the forked path. When the poet cranes his neck to look "as far as I could," it is as if we are looking with him. When he stands there deciding, we wait with him. In fact, the next two stanzas can be understood as what the poet is thinking about during this moment when "long I stood" trying to decide. If we understand the roads as different paths in life, the poet's problem becomes more urgent. In traveling one path, he forsakes the other; he thinks that maybe he can travel the other one later, but "knowing how way leads on to way, / I doubted if I should ever come back." He makes his choice: the path that appears less travelled.

The poem is less clear about the result of this choice, or if the poet's deliberation in making the choice was the right thing. For one thing, in the final stanza, he says, "I shall be telling this with a sigh," suggesting that perhaps he now regrets his choice. Secondly, the title of the poem, "The Road Not Taken," could mean that in choosing one road over the other, the poet has missed out on opportunities that he regrets. It's entirely possible that when the poet "stood long" to make his choice, he made the wrong one.