"Meeting at Night" is written in a very loose version of iambic tetrameter. This means that, theoretically, each line should contain four (tetra-) iambs (a type of beat that consists of an unstressed syllable followed by a stressed syllable – da DUM). Robert Browning, however, is no ordinary poet, and there is not a single line in the poem of "pure" iambic tetrameter; every line contains at least one substitution (the replacement of, in this case, an iamb with a different type of beat).
Take line 6 as an example, which is arguably the most regular line in the poem:
And quench | its speed | i' the slush-|y sand.
The first two feet (the divisions of a line of poetry) are clearly iambs, following the pattern unstressed-stressed (da DUM). However, the third foot (beginning with "i' the") contains two unstressed syllables followed by a stressed syllable (da da DUM). This is called an anapest, and nearly every single line in the poem contains at least one anapest (lines 1 and 10 are the only ones that don't). The final foot goes back to an iamb.
As one further example of the metrical variation on display in "Meeting at Night"), take the poem's concluding line:
Than the two | hearts beat-|ing each | to each.
The first foot (we've put in a vertical line to help you see the divisions better) is an anapest (da da DUM), but then the second foot is two stressed syllables (DUM DUM); this is called a spondee. The final two feet are iambs (da DUM). In this line alone, we have three – count 'em: three! – different types of beats represented. Browning makes good use of various metrical patterns to achieve different effects in the poem. Can you think of how this might affect the poem's meaning?
There are two other things that need to be mentioned with respect to the poem's form. First, it contains two stanzas of six lines each, for a total of twelve lines. This is dangerously close to a sonnet (which contains fourteen lines). While there is no reason to call this a sonnet, poems that come this close to being a sonnet should be given a closer look. Second, the poem has a very neat and contained rhyme scheme: ABCCBA ABCCBA. Here's an example from the first stanza:
The grey sea and the long black land; (A)
And the yellow half-moon large and low; (B)
And the startled little waves that leap (C)
In fiery ringlets from their sleep, (C)
As I gain the cove with pushing prow, (B)
And quench its speed i' the slushy sand. (A)
Notice how each stanza is bracketed by a rhyme (the A rhyme), and that there are two rhymes in the middle (the C rhyme), giving the poem a sort of palindrome effect (same forwards and backwards). It's almost like a set of Russian dolls or something like that, where each rhyme is nestled inside another rhyme.