In sonnet 18 how does the poet use rhyme to connect ideas throughout the sonnet?

Interesting question. This sonnet follows the standard so-called Shakespearean sonnet form, which means that its rhyme scheme is ABABCDCDEFEFGG. In this, it differs from other sonnets which might adhere to the Petrarchan rhyme scheme.
One of the key ways in which Shakespeare's rhyme scheme influences the meaning of all his sonnets is that it divides the poem, through rhyme, into three quatrains (sets of four lines), with the final two lines, a rhyming couplet, being set apart. Shakespeare uses this technique of denoting a conclusion with a rhyming couplet in his plays, too; he often brings a scene to an end with a rhyming couplet. In this poem, the final rhyming couplet serves to summarize the poem's message: anaphora ("So long . . .") in these lines also adds to the summative sense of the couplet. The two lines are connected through both structure and rhyme, bringing together the ideas of the preceding twelve lines.
In the first quatrain, ABAB, the idea of summer's brevity is discussed, with the rhyme words encapsulating this: "day," "temperate," "May," and "date."
The next quatrain, CDCD, discusses the shortcomings of summer: "shines" is a contrast to "dimm'd," while "declines" continues the idea presented in "dimm'd."
Next, the EFEF quatrain contrasts the potential decline of beauty and summer—"fade," "shade"—with the prospect of the beloved's beauty issuing a challenge to this decline: "ow'st," "growst." This quatrain serves as a precursor to the summative couplet which follows: throughout the poem, the key ideas the speaker is presenting are emphasized in the rhyme words. Indeed, it would be possible to construct a rough sense of what this poem is about using the rhyme words only, so carefully did Shakespeare choose these in order to draw attention to his most salient points.