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Don't give them a tutorial at all. Devise what you think is an ingenious and totally intuitive interface, preferably without a HUD or any on-screen indicators that would prevent the players' complete immersion into your brilliant universe. Make it so transparently obvious that no instruction is needed. Throw them in and wish them luck.
One of the games I had to judge for the Innovation Awards did exactly that. The UI left me nauseated -- its 3D first-person view weaved drunkenly around, apparently in an effort to convey the notion that my avatar was feeling sick and disoriented.
It worked; before long, so was I. It also took me five minutes of experimentation with its supposedly intuitive user interface just to figure out how to open a door.
The totally intuitive user interface has been a holy grail of human-computer interaction for decades now. I'll be blunt: there's no such thing. Unless you're making a computer game about using a computer, the machine's input devices are unlikely to correspond to the real-world activity that the game simulates.
I worked on Madden NFL as far back as the Sega Genesis days, and I can tell you that choosing a play, then snapping the ball, passing it to one of several receivers, catching it, and running with it are not trivial with three buttons and a D-pad. We did it very successfully -- but we still had to ship a manual with the game. There wasn't room for a tutorial in a Genesis cartridge.
The arrival of the Wii controller and more recently the Kinect has moved the issue to the foreground again, and some people are very excited about the possibility of Minority Report-style interfaces. These folks have forgotten -- or probably never knew -- why the computer mouse was invented in the first place. Touch screens are tiring to use for long periods, because you have to hold your arm up all the time. Waving your arms around, as in Minority Report, is even more tiring. It might look very swishy and cool, but you can't do it for hours on end.
Players don't need a tutorial as much if they have specialized gear, of course -- a high-end joystick for flight simulators (but they'll still have to press a key on the keyboard to lower the landing gear), or the DK Bongos for playing Donkey Konga. But you can't count on the player owning these devices unless you ship them with the game, and that means he still needs a tutorial or a manual for his ordinary controller.
Put simply, your user interface must map the machine's controls to game-world activities, and somehow, somewhere, you're going to have to explain that mapping. And your interface almost certainly isn't as intuitive as you think it is. You've been playing your own game for months or years, so it's second nature to you, but your players are new to it. They need a tutorial. Really.
Some of you might have noticed that this isn't very constructive criticism. I have identified a number of things not to do, but I haven't told you how to create a good tutorial. That's because it's hard to create general rules for a medium as diverse as ours is. A tutorial for a shooter game will necessarily be very different for one from a construction and management simulation. The best positive advice I can offer that covers all the cases is, be sure you try out your tutorial on complete novices -- and your game too, for that matter.