Watch the Olympics as the cameras go "backstage" and film the various athletes who wait their turns. While many engage in limbering exercise, they also listen to music, walk back and forth, meditate, pray, joke, talk to their coaches, etc. These activities are not unlike those in which actors backstage engage.
Well, if you look at the High School Musical Films, you can see Sharpay trying out a few relaxation techniques that look as if they could be karate moves and making violent sounds! But seriously, when I was doing lots of acting the kind of relaxation techniques that we used varied from person to person and also depended a lot on the director. For one play I was involved in, the director got us to dance altogether to a track of music before letting the audience in. Others got us to sit in a circle and count up to twenty with our eyes closed before each rehearsal, or got us to do stretches. Other friends who acted would do some kind of chanting or yoga. In a sense, it doesn't really matter what you do, as long as whatever it is helps to relax you and focus on the performance ahead.