Each of these poets had a distinctive style expressive of his own brand of Romanticism. We can discuss them separately, and you might then draw conclusions as to the common threads among them and how each one in his own way was a part of the Zeitgeist—the spirit of the time.
Wordsworth laid out his aesthetic in the preface he wrote for his and Coleridge's collection Lyrical Ballads. For Wordsworth, the most important requirement of the new kind of poetry he aimed to write was that its language should be simple and direct, avoiding artificial "poetic diction" and essentially being the same as prose apart from meter and rhyme. Though Wordsworth did not identify it as such, this was a kind of "democratization" of poetry, an expression of the new egalitarian ideals of his era of revolution and social change. The degree to which personal emotion is expressed in his verse was also a change from the past. Wordsworth's The Prelude is a long autobiographical poem written in direct language and inwardly focused. In Wordsworth's work overall, we see the prime Romantic traits of naturalness in language and self-expression.
Coleridge's work is expressive of a side of Romanticism that is, oddly enough, in some ways the opposite of Wordsworth's. His focus, in his best-known poems, is on the exotic, fantastic world of legend and the past. In "Kublai Khan," he relates a kind of fairy-tale of "the Orient," inspired by an opium dream. As with his "Rime of the Ancient Mariner," the emphasis is on the supernatural and on ideas usually buried in the subconscious, in which there is no clear division between reality and illusion.
Shelley and Keats were a generation younger than Wordsworth and Coleridge. Their work thus represents a second phase of the Romantic movement, in which the aim was no longer self-consciously to produce groundbreaking works in a new form, but rather to express (and to place the reader in) a heightened state of emotion, an exalted artistic experience in which there is an immediacy of expression not seen before in literature. In both poets, the language becomes an almost musical tapestry, with rich, startling word choices and uninhibited emotion. These two writers developed further the features of the earlier generation's work which we have described, adding their own idiosyncratic expression and the force of their own personalities to create their unique styles.