You can't, if you're talking about the boot chime. That can only be silenced by muting the volume. I suppose if you wanted to do something that I would consider supremely stupid and find some program to tinker with the PRAM, it'd be possible, but as I said, I'd consider it supremely stupid to do that.
All other sounds appear to be an all or nothing sort of deal. So if you go to the sounds setting in system preferences, there's a sound effects tab, and then there's a checkbox about playing user interface sounds. Untick that, and then you have eliminated all but the boot chime, which you'll just have to live with.
I suppose you could consider paying someone to write a simple script that is run at shutdown and another at startup, that mutes and unmutes the volume respectively. I wouldn't recommend it, because it would require editing of some of the core Unix system files. Any tiny little mistake could have some really nasty consequences, not to mention the possibility of knock on effects the next time there's an update like 10.7.2.
Could you pls tell me how to turn off the start-up and close sounds? I've turned off all the other sounds my computer makes but can't get those.
I realize I could simply mute the volume but I would rather turn them off for convenience.