A sonnet has both a physical structure, and an underlying way of structuring the exploration of an idea.
PHYSICAL STRUCTURE:
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A sonnet is composed of fourteen lines. Each line has exactly ten syllables, which have alternating weak and strong stress, e.g. "shall I comPARE thee TO a SUMmer's DAY." Each unit of an unstressed and a stressed syllable is known as an "iamb," and there are five of them in a line, so this pattern is known as "Iambic Pentameter" (from "penta" meaning "five," - as in the word "pentagon" meaning "five-sided").
The fourteen lines are arranged in a rhyming scheme of three quatrains, and one couplet, thus: ABAB CDCD EFEF GG.
COMPOSITION:
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Formal sonnets explore an idea, sometimes phrased as a question or a statement in the first line.
The first eight lines of the sonnet explore the idea from one viewpoint. For example, in Shakespeare's sonnet "Shall I compare thee to a summer's day...," Shakespeare does just that for the first eight lines.
However, after the first eight lines of a sonnet, there is a change of perspective, known as a "volta". The third set of four lines provides a different way of looking at the idea explored by the first eight. Sometimes, it is a complete refutation or rebuttal of the original idea, but more commonly, it is is just an expansion of the original idea. Thus, after Shakespeare has compared the subject of his sonnet to a summer's day for eight lines, he begins the ninth line: "But thy eternal beauty shall not fade..." and continues on to basically say why she is not only fairer than summer, but will also last eternally.
The last two lines in a sonnet provide a summary of the idea that has been explored, usually with a strong reference to the third quatrain.
There's more to a sonnet than 14 lines that rhyme. :) I hope this helps! I write a lot of poetry, but sonnets are my favourite form to write in. :) Here's one of mine, which uses all of the principles I describe above...
The Grasshoppers and the Ants
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All summer long they strained, load after load,
And scoured the fields for food to lay in store:
The little ants who combed the dusty road,
And saved the crumbs that lay upon the floor.
All summer long the lithe grasshoppers laughed
To see the ants thus toiling to prepare:
For surely so much labouring seems daft
When easy pickings are found everywhere!
But winter came far sooner than they thought,
Blew colder than they ever could have feared:
The ants, who'd done their homework, suffered nought,
The grasshoppers starved, died and disappeared.
There's always something gained in honest work:
The seasons' test will claim all those who shirk.
:)