In terms of structure, a Shakespearean sonnet has 14 lines and is written in iambic pentameter. This means that is has 3 quatrains (4 line sections) and one heroic couplet. The rhyme scheme, therefore, is abab (quatrain 1), cdcd (quatrain 2), efef (quatrain 3), and gg (heroic couplet).
Like a Petrarchian sonnet, Shakespeare usually presents a problem in the first octet (8 lines) and a solution in the sestet (6 lines) with a volta (a turn) in line 9 which transitions from problem to solution.
There are some exceptions to this break down. Sometimes only the couplet can contain the solution. In Sonnet 116, for example, Shakespeare gives the solution early ("it is an ever fixed mark") and develops his answer throughout the sonnet. In any case, most of Shakespeare's sonnets deal with the themes of eternity (of art and artist). Here are a list of other questions to ask yourself:
1. What is happening in each quatrain? Are there shifts between each quatrain? Do the quatrains build on each other?
2. What purpose does the couplet serve? Is it a conclusion, or does it restate a message in the sonnet, only in stronger terms? Does it refute anything from the above 12 lines? What finality does it provide?
3. Does the sonnet begin with an image or "scene" from the external world? Does it use an extended metaphor throughout?
4. How does the sonnet form a wholeness from the sum of its parts? What is the speaker's overall message? Does this message resonate in the internal and external world?
Also, here's what I have from a set of killer lecture notes I've used in the past: (see link below)