Read and reread the performance script. If the performance is to be improvised, study your character's specific mental condition and the physical mannerisms attributed to it. If you simply go onstage and randomly start acting "insane" -- yelling and ranting without an educated and researched point of view -- you will end up acting out multiple mental conditions, which could become cumbersome and not engaging.
It is important to look the part as well as act the part. Depending on the condition, wear your clothes slightly askew or disheveled. Study the mental condition of your character and see how patients of the condition regard their clothes and appearance. When applying makeup, keep in mind that theater makeup application is always slightly overdone, as your audience will often be at least ten feet away. When playing an insane character, ramp up the makeup application; bring attention to the eyes and perhaps put on lipstick that is (purposefully) misapplied.
Your performance should not be obvious or reveal too much; the audience should be able to pick up on the notion that your character is a bit "off." Never outwardly say things such as "I feel crazy" or use psychological terminology, since a person with a specific malady will likely not understand his own psychosis.
Practice your insane character before your performance, either in front of a mirror, with friends and colleagues or even out in public before unsuspecting strangers. Commit to your character, using the unusual mannerisms that your character would -- such as, perhaps, rubbing off spots on your shirt that aren't there or turning your head in paranoia -- and repeating.