Leo says being anonymous isn't the same thing as being secure. He can be anonymous and not secure on the net, and vice versa. How can Jimmy be more secure while? Leo says a good place to start is with TWiTs netcast Security Now. There's security issues popping up all the time and the only way to be completely secure is to stay off the internet. That really isn't practical in today's information age. There's a great source for tips on security at US-Computer Emergency Response Team (US-CERT). Also, don't fall for social engineering where he would get an email or phone call from "Microsoft," saying they see viruses on his computer. Microsoft will never contact him.
The US National Security Administration (NSA) has some great Security Configuration Guides on how to secure access as well. They have a program called STOP-THINK-CONNECT. We pay for this stuff, he may as well take advantage of the information they provide.
Also, get a router. Routers are great buffers. They're dumb boxes that reject most incoming attacks. Turn on WPA2 encryption on the wireless router. Give it a really hard to guess password that has alphanumerics. He should also change the SSID (name) of his router to something cryptic (most are set to "Linksys"). Disable UPnP. And it's very important that he keep his OS and software up to date, especially browsers, Adobe reader, and Flash.