Decide which Shakespearean castle you will be drawing. If you are drawing the seat of Edward IV's court in "Richard III," have a look at medieval Norman castles, such as the one at Bromburgh. Richard Neville, the historical Richard III, took this castle in 1464. If you are illustrating "Othello," or any of the many plays that take place in Italy, study the Doge's Palace in Venice, a Gothic structure built in the late 14th and early 15th centuries.
Read carefully all lines and stage directions that refer to the castle you have chosen. Shakespeare's settings are notoriously vague, but you can sometimes find clues that will help you in your illustration. Act 1 Scene 1 of "Hamlet" makes it clear that you will need to draw extensive battlements for the night watches to patrol. A careful reading of Act 3 Scene 3 of "Richard II" reveals that a single wall must, on one hand, be large enough for Richard, Carlisle, Aumerle, Scroop, Salisbury and all their heralds and attendants to stand on, while lying close enough to the ground to allow Northumberland and the king to converse easily.
Determine the period in which the play takes place. If you have a print version of Shakespeare's complete works, look at the introduction to the individual play you are illustrating. "The Merry Wives of Windsor" features Falstaff and the titular housewives at work and play in Shakespeare's own Renaissance England, while "Titus Andronicus" takes place in the 1st century B.C.
Get a sense of the mood and theme of the play you are working with. The Navarran palace in which Ferdinand and his companions hole themselves up in "Love's Labour's Lost," for example, demands a light and airy representation, while you should consider something stark and heavy for the Scottish fortress where Macbeth and Lady Macbeth commit their grizzly murders.
Track down images of castles that match both the period and feel of the play you are illustrating to use as models. If possible, sketch from life, feeling free to add or subtract from what you observe in order to match the mood of the play.