... and demands some form of payment. How does it work?

Over the past 10 months, there have been at least 2 appearances of Trojans which can force people to pay ransom money. No, they don't kidnap close relatives. Instead, these trojans encrypt files on the infected computer. A $300 payment will have them decrpyted and unlocked.

So not only must you have updated antispyware and antivirus software running, but also your backups must be current and working.

If you backup your data daily, then who cares (apart from nuisance factor) if your files are encrypted?  You can always restore from the backup.

For good free backup software, which will work with a CD writer and DVD writer, visit http://www.simplysafebackup.com/