A shutter press while in ALT mode starts the currently loaded script.
So, start up your camera normally, shortly press the alt key (whatever it is in your camera) to enter ALT mode and then fully press shutter.
You know you're in ALT mode when there's some text in blue background in the bottom part of the screen, unless CHDK for your camera has bugs/problems with screen refreshes.
The above will probably make the default script start unless you've managed to load another script. Pressing func/set while in ALT mode will bring up the script menu where you can load up another one and change settings for the currently loaded script. However, this menu has nothing to do with starting the script.
ALT mode is NOT like the ALT key on your computer. It's more like the CAPS LOCK key. Basically ALT mode is there for configuring CHDK, using some CHDK shortcut keys and for running scripts. It's not for everyday photography, and CHDK does most of its magic outside ALT mode.