The only time you can actually know your computer is completely secure is when your computer has just had its hard drive completely wiped, is disconnected from the Internet, turned off, unplugged, and locked in a vault to which only you have the key.
More realistically, if your computer is a more normal computer up and running and connected to the Internet, even the most competent anti-malware applications, hardware and software firewalls, routing schemes, and even encryption are inadequate to ensure that your computer and data is COMPLETELY secure, because there is no such thing as genuinely complete security. This is true whatever kind of computer you may use, whether it's a PC, a MAC, a Linux box, or whatever.
This is why you as the user must remain vigilant and always do your best to monitor your computer's behavior. Understand that merely because you cannot ever achieve the serenity that comes with such complete security does not mean that your computer is or will become compromised or infected. There are a few simple rules that, if you follow them, they will keep your own personal computer reasonably safe in the real world.
1. Use a competent antivirus application and keep it up to date. Norton (the new version) is probably the best, but there are many competent freeware versions around. For years I used AVG; later I used Avast on my older, weaker machines because AVG got a bit bloated. Now I use Norton on my more modern computers and, on my older single-processor machines, Panda Cloud, which is an interesting new cloud-based system that should keep itself updated better than others and, because much of it runs in the cloud, it is particularly clean and tidy on your machine and doesn't slow it down. Of course it needs to be connected to the Internet to operate.
Whenever you notice your computer behaving abnormally you might want to run a full antivirus scan.
2. Periodically run an anti-adware, anti-spyware scan using something like Lavasoft's Ad-Aware and/or Spybot Search and Destroy, both available for free. Note that both find things the other does not.
EVERY computer that ventures out onto the web has some adware and spyware -- there is no reasonable way to avoid it. Don't be alarmed when these programs indicate you've been hit by these, even a LOT of these. They most often consist of such relatively harmless items as tracking cookies that advertising and marketing sites put onto your computer. When these minor "infections" become too numerous, however, they can slow your computer down so it is best to scan for and remove them once a month or so.
3. Get a router, even if you have only a single computer. These protect you from the worst threats from the outside.
4. DO NOT IGNORE ANTI-MALWARE WARNINGS!!! If your antivirus or browser application warns you about some website or application, BELIEVE IT unless you have STRONG reason to do otherwise. DON'T GO THERE!!!
Note that some bad guys will reassure you, warning you in advance that your anti-virus will go off and to just bypass the warnings, because everything's really OK. If you believe that, I've got this property on the banks of the scenic St. John's River in Central Florida that you would LOVE to buy, but don't go look at it right now, OK. Just give me your check. (And if you don't like that, check out this bridge between Brooklyn and Manhattan -- a SURE moneymaker for a discerning investor like yourself!)
5. NEVER, EVER, EVER click on an executable file you have received in an email even if the email appears to have come from a friend. This is the chief way people's PCs get turned into zombies for spammers' botnets, but the damage they can do is not limited only to that sort of thing.
Executable files are those with such extensions as .exe, .bat, and .scr (and too many others to list -- those are just the most common). Other files can also be infected, including .pdf and .doc files, and more frequently now .zip files.
Note that website links can also throw infections onto your machine (or more usually link you to sites that will help the bad guys steal your identity no matter HOW real they look) so be careful there. Most modern email clients warn you when the apparent URL differs from the actual URL of the link. When in doubt, go directly to the company's website and do not do so through the link in the email.
.jpg and .gif can generally be considered safe.
6. (Assuming you have a Windows machine) Install Microsoft updates the second Tuesday of every month. ALWAYS keep your operating system up to date.
Please understand that many people are too paranoid. If you follow those simple rules above it is almost certain you aren't going to get hit. Remember, none of the bad guys, nor the government, really wants to read your email.