In your admin panel under settings -> system configuration, you have an option to supply IP addresses to ban.

You can find IPs by editing the profile of a problem user to find their recorded IP, or by editing a link to see the submitter IP. You can also find IPs of people rating articles, by clicking the 'show individual votes' link below the article.

You may wish to use http://visualroute.visualware.com to trace an IP to its origin, and http://www.arin.net/whois to check what IP range a particular ISP uses.

Note that you can ban ranges. Banning the IP 12.25.36 will also block 12.25.36.43.7, etc... if what you type in the IP ban box matches the begining of the IP, the IP will be banned.

You can also select if you wish to ban these IPs from the whole site or simply from the member registration page. Since in banning an IP range you may often block a few innocents, if there's no harm people can do to you without being logged in as a member you may wish to only block the IPs from registration. On the other hand, if you allow guest submissions so that the person can still cause you much trouble without having a user account, you'll need to block from the whole site.