What's the best way to prepare for a speaking exam?

Confidence is key, and confidence comes, more often than not, with practice. Therefore, I would recommend printing out some of the practice questions from the exam board's website (provided their available) and getting a friend/family member/a tutor (they don't necessarily have to speak Spanish) to ask you the question on your card and listen to your answer. This fact-to-face, one-on-one dynamic will prepare candidates for the environment they'll be sitting the actual exam in. Speaking aloud to yourself, or anyone else, in Spanish is an ideal way to improve one's accent, intonation and pronunciation. Spanish can be a particularly tricky language to speak clearly in, so practising speaking calmly, slowly and thoughtfully to yourself can be really helpful in practising this.
In terms of knowledge of the language, I would avoid trying to learn large chunks of prose off by heart, but instead would learn some key conversational phrases and idioms which give the speech fluency and a natural feel (e.g. 'pues' (well), yo diría que (I would say that), 'me da igual' (I don't mind)). It is also helpful to learn such phrases in order to demonstrate knowledge of tenses.