The arena experience at hockey games can be overloaded at times. There are giveaways, prompted cheering from the scoreboard or loudspeakers, in game hosts, and even cheerleaders and paid superfans are entering the arena. Some of these things are fine, and serve some purpose, but if you've ever been to an arena where this is essentially all fans do for cheering, other than modestly celebrating a goal or groaning/whining about a penalty, you can come away kind of empty.
Some teams have songs, traditions, cheers, that allow the fans to just have a good time by their own design... but not every team or rink has these. Creating a tradition can be difficult, and it may take more than you and your group of family/friends to have it catch on. I can't make a suggestion for what would work in your rink, but there is one thing I'll suggest to anyone at a game: Have fun, and don't fear embarrassment.
Sing. Dance. Cheer. Heckle the opposition. Make signs. Dress up. Paint your face. Give players nicknames that don't just add 'sy' to their last name. If you can, buy a drink or two. Get your butt out of your seat on occasion. Talk with the people around you. Find an after game hangout to celebrate wins and overcome losses. Bring new and different people to the game to keep the experience fresh. Throw the snake, Travis. Don't try and keep your cool just because your boyfriend/girlfriend is with you. For any corporate types out there, conduct any business you need to do that night during the intermission, and tell your associate to have fun when the game is on.
Ride the wave of completely irrational fandom. Suspend your analytical side for sixty minutes. You're allowed. It's your ticket. Be appreciative of the opposition, but don't get TOO excited over the fact you're getting a rare chance to see Ovechkin or Stamkos in person... you've still got a team to support.
There are ways that the fan enhance the fan's experience that are out of the fan's control, but the ability to have fun is really in the control of the individual. Give your team, and your arena, the best you have to offer. Don't let yourself feel cheated out by the price of the ticket (for some games/rinks, that's easier to say than do, I realize), please don't just sit there and wait for something to happen. Help make it happen. Give your team extra incentive to block that shot and beat the opponent to the lose puck. Make your team want to play in their home rink more than anywhere else.
You have that ability. It's your choice, maybe your duty, to utilize it.
Most of all, don't be a suck.