"Ulysses" is a dramatic monologue, a poetic form we usually associate with Robert Browning, a Victorian poet and contemporary of Tennyson. A dramatic monologue is a poem spoken by a single person (mono-) to an audience; that audience could be one person or a group of people referred to in the poem (at line 49 Ulysses says "you and I are old") or any other implied audience. A monologue differs from a soliloquy (which also has one speaker) because it is spoken to an audience that is a part of the situation, as opposed to the audience in a theater. A dramatic monologue is identifiable by the fact that it resembles a conversation in which you can only hear one person talking; the speaker seems clearly to be responding to someone, but that person or group doesn't actually speak in the poem.
As far as meter goes, Tennyson was an expert metricist, but in this poem he keeps things pretty simple, sticking with the standard meter of English, iambic pentameter. That means each line has five iambs, or feet: each iamb contains an unstressed syllable followed by a stressed syllable, as in: "To strive, / to seek, / to find, / and not / to yield" (70).
Even though the poem is mostly in iambic pentameter, Tennyson frequently throws in different types of beats. For example, line 69 begins with a beat that contains two stressed syllables: "Made weak." A beat with two stressed syllables in a row like this is called a spondee. Other examples of spondees occur in lines 44, 45, and 67.
At other moments, Tennyson will use a beat that contains a stressed syllable followed by an unstressed syllable, as in "Life to" (7). This is called a trochee. Tennyson varies the meter of his poem periodically because it is a dramatic monologue; nobody speaks entirely in iambic pentameter, and the changing beats give the poem a more realistic feel, so it seems more like somebody is actually speaking.