I mash a ton of buttons when tanking. There's often more to it than just following some preset order of button mashing, however. You need to understand the abilities you have, and how much threat they generate, so that you can use them as they come available to you (i.e., off cooldown).
As others have mentioned, generally a group will want the tank to lead. Leading means marking mobs for kill order, or cc, or whatever your strategy for defeating them may be. My rule of thumb is healers first, then casters, then ranged dps, then melee dps. But you will come up with your own. Always make use of your available cc. In some cases you may have to try and tank 4 mobs at once, but that's not ideal. Use as much cc as you possibly can, and try not to break others' cc (such as with thunderclap when you're too close). It's probably obvious, but typical cc methods include: sheep (mage), trap (hunter), seduce (warlock), and sap (rogue). Use the mob markers (available in the drop down box if you click on the mob) to identify which target is sheeped, sapped, main target, second target, etc. And stick with the scheme!
Learn how to pull, because in most cases you will be pulling (occasionally a hunter can misdirect pull for you, but it has a cooldown and if you're in a groove you won't be able to use it consistently). This can mean pulling via line of sight, to grab casters, charging in, or standing at range and pulling with a bow/gun.
After the pull, the real fun begins. This is where the button mashing happens, and you have to know what you can and should do, and then react accordingly. Being a tank means being in control of the action, which can be a lot of fun, or it can be really frustrating. I wish you the best of luck. /salute!
Marroweater