There's no easy segue into this: There are bad people on the internet.
By being a public figure (and honestly, if you've written anything and been published anywhere, you're a public figure), you are a target. A panel I attended at Mo*Con covered a lot of how to protect your life when you live online, and the principles of how to balance privacy and real life.
Slightly overlapping on the Venn diagram of keeping yourself safe are the technical aspects of keeping your online life secure. There's a lot to know. Even a rough overview covers having good passwords, encrypting your web browsing, knowing the how to effectively back up your data, social engineering, and keeping yourself off of stalker-friendly "people searches".
I hope the article below, which originally appeared in Volume 47, Issue Two of the SFWA Bulletin1, helps you keep the creepers a little farther away.
1 Presented with permission. Please link back to this document. Thanks.