English sonnets are 14 lines in length and consist of stanzas made up of three quatrains with alternating rhyme and a single couplet at the end. A quatrain is a stanza or verse consisting of four lines; the couplet at the very end only has two. The rhyming works by keeping those rhymes within their own stanza, following the ABAB model. The rhyming doesn't carry over from one stanza to another. Instead, the second stanza uses its own rhymes, as does the third stanza and the couplet at the end.
The Italian sonnet follows a similar pattern to its English cousin and uses 14 lines as well. The first stanza or verse is made up of eight lines, also known as an octave, and rhymes by following an AABBAABBA pattern. This means the first two lines rhyme, lines three and four rhyme and so on. The concluding six lines are very flexible in how they're written and can follow just about any rhyming pattern the poet desires.
The villanelle uses a total of 19 lines, consisting of five tercets and a single quatrain. A tercet is a stanza of three lines. The rhythm and rhyme of a tercet within a villanelle follows the ABA pattern, using a pattern of ABAB for a quartrain at the end. In most cases, the villanelle starts off with a very strong first stanza and then builds in intensity from one stanza to the next.
One of the harder patterns to follow, the sestina doesn't use rhyming as its main tool. Made up of six-line stanzas, the words that each line in the first stanza end with appear in a rotating fashion in the stanzas that follow. For example, if the first line of the first stanza ends with "sheep," then "sheep" will show up in every stanza that follows at the end of one of six lines. The position where "sheep" appears rotates, so it doesn't show up at the end of the same line more than once. The sestina is then closed by a final tercet using the repeating line-ending word throughout.