Watch to see if the performer's lips are consistent with the music. If there is a noticeable mismatch between the singer’s lips and the vocals then that singer is lip-syncing.
Listen to the sound of the instruments. If there are three musicians on stage and it sounds like a 100-piece orchestra, then it’s probably a prerecorded track.
When the performance includes dancing feats such as hanging upside down from a wire and doing back flips while the artist is belting out a tune, mostly likely the artist is performing with a recorded vocal.
Most live performances have a slightly different sound that is not so studio perfect but is reflective of the live instruments and vocals. If a live performance sounds exactly like the recording you have at home, it probably is.