I dont know if you already do this but riding with friends can really help. Even riding with a trainer we can get nervous, but sometimes if a friend is there it can help to calm your nerves. Even just knowing that you being tense will not help is good. It is hard not to anticipate, but try to trust the horse and just focus on rhythm and what is happening next.
Talking out loud is definitely helpful and keeping a positive attitude as well. Put crackers in your hands so if you tighter them they break, you could also put dollar bills underneath the balls of your feet in the stirrups. When you tense you legs instinctively tighten and go slightly up as well as bringing your heels up. If you did that with the dollar bills underneath your feet you loose the dollar ;)
The most basic thing you can do is breathe. Many times when someone tenses up, they forget to breathe. If you feel yourself getting stressed, take big, deep, deliberate breaths and focus on them. It's incredible the difference it can make.
Singing or talking to yourself is also meant to help calm both you and your horse.
Another thing that can help is thinking forward. Concentrate on your next move and prepare for it instead of worrying about what's happening right now. It's not a particularly effective thing to do in terms of performance but it can help with nerves.