How is over the air access to Internet Radio Linking Project (IRLP) nodes accomplished?

The Internet Radio Linking Project (IRLP) allows amateur radio operators to connect repeaters across the world via the internet. To command a local IRLP node to connect to a distant node, you use the keypad on your radio to transmit Dual-Tone Multi-Frequency (DTMF) signals. These are the same familiar 'touch-tones' used on traditional telephones. While CTCSS tones are often used to open a repeater's squelch so you can transmit through it, DTMF tones are specifically required to 'dial' the node numbers and issue commands. Over-the-air voice passwords or internet passwords are not used for this standard radio control method.