You can hear each sound by clicking on his IPA transcription.
Alveolar tap. The alveolar region serves as the target for the tongue tip, which vibrates there briefly before falling back to rest against the lower teeth (see figure 3.29 below).
Retroflex tap. The tip of the tongue curves up and back, and its underside vibrates briefly against the roof of the mouth, before falling back to rest against the lower teeth (see figure 3.30 below).
Velar or uvular tap. Here the body of the tongue serves as the site of vibration: the soft palate or uvula vibrates briefly against it (see figure 3.31 below).
Alveolar trill. The alveolar region serves as the target for the tongue tip, which vibrates there under pressure from the airstream behind. The vibration produces occlusive sounds and vocalic-type resonances in rapid alternation. This is the famous "rolled r" of Spanish and other languages (see figure 3.29 again, reproduced below).