The attacker types in Port 139, or Port 8080, or any other port number, and the target's IP number, and then clicks the Nuke button. Nuking is NOT an IRC attack, since it does not use the IRC servers or network. But it is common on IRC because that is an easy place to obtain other people's IP numbers. When people are nuked they often worry that they are being attacked by someone with superior computer knowledge than they have. But it takes no skill whatsoever to nuke someone.
Nuke programs are simply point and click programs that any newbie can use.
It is easy to upgrade your Win95 system so that it becomes un-nukeable. All you have to do is install the special Microsoft bug fixes or upgrades listed below. If you are running Windows 3.1 or Windows98 you do NOT need to worry about nukes. Install wsockupd.exe by running it. Install msdun13.exe by running it.