Both the Petrarchan and Shakespearean sonnets consist of fourteen lines and are written in iambic pentameter.  This means that each line, generally speaking, will have five (penta-) feet, with each foot consisting of one unaccented syllable followed by one accented syllable: this means that each line will typically have ten syllables.  The foot name is an iamb (this is where we get the word iambic), and each iamb has two syllables: one unaccented followed by one accented syllable.  

The Petrarchan sonnet is divided into an eight line octave (rhyme scheme: abbaabba) followed by a six line sestet (with a rhyme scheme that is more open: cdcdcd, cdecde, cdeedc—really, any combination of "c"s and "d"s and maybe "e"s is acceptable).  Then, there is usually some division of content between the octave and sestet.  The octave might pose a question that the sestet answers.  The octave might present a problem that the sestet solves.  The octave could present an issue from one angle, and then the sestet takes a different angle on the issue.

The Shakespearean sonnet is divided into three four line groups called quatrains (rhyming ababcdcdefef), followed by a rhyming couplet.  Each quatrain might present an example, and the couplet could present whatever ties the examples together.  Each quatrain might ask a question with the couplet providing the one answer to them all.  Generally, the couplet contains some key information that we need in order to understand the importance of the quatrains.

The Italian term sonetto simply means a short or little song. The fourteen-line sonnet form with which later became known as the "Italian" or "Petrarchan" sonnet appears to have first been regularized in the work of Guittone of Arezzo, a thirteenth century Italian poet. Petrarch (1304 – 1374) employed the form in his 366-sonnet sequence, Rime Sparse, a collection of poems on the subject of his love for a woman named Laura. Sir Thomas Wyatt (1503 – 1542) and Henry Howard, Earl of Surrey (1517 - 1547) translated Petrarch's sonnets into English and are generally regarded as the founders of the English sonnet tradition. Wyatt, in particular, used the Petrarchan sonnet form extensively in his own poetic works as well as his translations. Although Surrey and other poets of his period wrote English sonnets, due to the fame and influence of Shakespeare's work, the English sonnet is frequently called a "Shakespearean" sonnet.

Both forms are fourteen lines long and normally written in iambic pentameter in English. They differ in both rhyme scheme and structure.

The Italian sonnet consists of an eight-line octave followed by a six-line sestet. The octave is rhymed as two closed quatrains, ABBAABBA. The sestet has a more flexible rhyme scheme, using two or three rhyme sounds, with common possibilities being CDECDE or CDCDCD. Its main structural feature is a "turn" or shift of focus between the octave and sestet.

The Shakespearean sonnet consists of three open quatrains followed by a couplet, i.e. its rhyme scheme is ABAB CDCD EFEF GG. In a typical English or Shakespearean sonnet, each quatrain has an individual theme, and then there is a break before the couplet, which can then either summarize the sonnet or work as a sort of surprise ending. Sometimes there is a minor turn after the second quatrain as well, but this is not an essential feature of the form.