Never log in to online banking sites from public networks and share important information on insecure connections. Everything you do is recorded and logged and the administrator of the network can look at this at anytime. Also other people could be watching your activities with Trojans, spyware etc.
Use different passwords for all sites and use uppercase and lowercase and numbers. The more random the better and the more likely it can’t be brute forced or dictionary attacked. You could also slightly encrypt your passwords with a hash or anything you want all sorts of stuff you can do to make passwords stronger.
Protect home computers by closing your network. You can do this by changing the name, making it private or hidden, also disable features like wireless and making good strong administrator and other passwords. Strong administrator passwords make sure no one can get into your configurations and setups. Strong network passwords makes sure no one gets into your network. Also enable WPA encryption or WPA2 encryption for best protection.
Invest in a power cell/ battery backup and always make backups sometimes one offline and one online. Security starts here the power cell is to protect from lightning damage and power-outages and the backups are to insure your information is safe and in more than one place.
Only give out social security numbers or credit card numbers on a secured website by seeing “https.” not “http” in the URL field. The extra “S” at the end stands for “secure” basically. Always look at the URL field, it might not even be the same website your originally visited that would be called “phishing” and that’s the most simple and common ways to capture usernames and passwords collectively.
Be careful when you share information with any site or person on the Internet. Who knows who might be trying to social engineer you into giving them all your passwords and recovery questions.
Always have some sort of firewall or antivirus and a backup cleaner. A good firewall or anti-virus is always a good thing on windows based machines and should prevent programs being automatically installed and prevent changes to your machine. A cleaner would help fix other problems on your computer and network and make it faster and safer.
Automatically delete cache, setup browsers to automatically delete history and password protect your keyring. This will normally make browsing and computing faster and to hide your history is just a smart thing to do just in case someone looks at all your recent websites. Password protecting your keyring will make all your other passwords more secure.
Install a hidden web server that automatically connects when connected to the internet. This is so you know when your computer goes online in a different location you can have a trace back to it and ping the new IP address. For more experienced users you could install a Trojan so you can see exactly what is going on and collect a bunch of information for your own investigation.
Have proof of hardware with pictures and/or documentation. Always know your serial on your computers and keep receipts. If you don’t have this then authorities can't help you and your all on your own.
Source: Hellbound Hackers, the computer security community and forum.