The short, pithy answer is that you don't. There is some extremely stealthy malware out there. Look at stuxnet, flame, and some of the banking trojans as examples. If a sophisticated enemy is out to get you chances are you won't know you've been hacked.
That being said it's extremely unlikely that you are ever going to be targeted by anything that sophisticated. Chances are you are like the majority of people trying to defend themselves against an average level of threat, in which case you do what we all do:
- patch your system. Most of your typical hacks target well-known vulnerabilities that have been patches for weeks, or even years. They target OS vulnerabilities but also adobe flash, java, adobe reader, etc. Make sure that you patch all your software as soon as patches come out
- Install a good AV and run scans frequently (looks like you've got this covered)
- narrow your system's attack surface. The more software you have installed the wider your attack surface is, so uninstall all software you don't use, especially the crappy bloatware that most out of the box systems have installed
- harden your system. Ensure that you have no guest accounts, and that all accounts have strong passwords. Turn off any service or process that isn't needed
As for knowing if you've been hacked it's usually pretty obvious unless you have been infected by stealth malware: you'll get pop-up ads, redirects to sites you didn't intend to visit, threatening messages telling you to pay money or have your life destroyed, your fiends will tell you that they are receiving spam from your email address, somebody in Timbuktu will buy a laptop using your credit card details, and you'll find out that somebody's used your personal information to apply for 40 different loans completely destroying your credit rating, or someone will siphon your life savings into a cayman islands bank account.
Good luck, and happy browsing.