How do you keep an audience involved in a performance? Answer using examples of specific acting techniques.

There is an assumption in theatre that the mere presence of actors, together with the attraction of story-telling and the psychological attraction of characters being imitated onstage, are enough to hold the witness’s attention (“witness” is the preferred term, rather than “spectator,” for a single member of an audience).  However, in the real world of the theatre arts, the actor uses several techniques to gain and hold the witness’s attention and interest, depending on the style of acting the cast and director employ.  For example, the Meisner technique of rehearsal and performance (named after the acting teacher Sanford Meisner) asks the actor to listen intently to the other actor’s on stage, in order to bring immediacy and believability to the conversation, thereby magnifying the effect of real-life activity.
In another style, called histrionics, the actors intentionally exaggerate all their actions and dialogue with the end-result of magnifying the action, so that the witness is enjoying a “larger-than-life” experience.  This style is largely out of date now, ever since Realism as a dramatic style emerged in the early 20th century.  It still can be seen in burlesque, parody, and highly stylized historical recreations, including opera.
In another style, which can be called naturalistic, the actors “forget” their fictive situation, and seek to convince the audience members that they are witnessing an actual event. In the Romantic era, this style called for “a willing suspension of disbelief” from the audience; that is, the audience was tasked with “forgetting” that they were in a theatre, and accepting the “fourth wall” idea of a proscenium stage.
In addition to acting techniques, the director (and the playwright) rely on the rhythms of the performance -- fast, slow, tense, relaxed, etc. -- to hold the audience's interest.