TCP is right though. If you pull the live and neatral pins from the plug (thats what we call what we have in the UK), then you are left with just the ground. That way the machine can discharge but there is nothing charging it back up again. That should discharge quicker than just leaving it.
I'm not familiar enough to know whether pressing the power might speed it up even further in this case.
Wouldn't plugging it into a socket which is powered off have the same effect? It would seem pointless to have the ground connected to the on/off switch.

Essentially you just have to short the anode to ground. You will have no trouble spotting the earth strap if you take the case off, the anode is under a rubber cap at the point of the rear of the tube. Right in the middle with a big cable attached to it. You just have to poke something metal (with a plastic handle) under the rubber cap, and attach it (usually with a crocodile clip on a wire) to ground. You can attach the clip first then just poke the anode and you're done. A long screwdriver is perfectly good for this.

Its worth noting that discharging a CRT is the one act of computer repair for which you should NOT wear a grounding strap. If you are particularly worried, stand on an old tyre or a rubber mat while you are doing it.
Don't expect the earth to move. I believe if you hunt around you will find another thread detailing the anti-climax that is discharging a CRT.