My computer has been invaded by something calling itself Winweb Security. I have Norton 360 so I can’t imagine how it made it through my firewall and internet security. I did an online search and it came back with way too many options for me to feel safe about which one go with. How do I know that what ever method I find posted to remove it is not actually something that will enable further damage to my computer???

in safe mode F8 run malwarebytes anti-malware and SUPERAntispyware,and what they find you
delete it manually. then run ccleaner to clean your pc, and mvregclean, to clean registry.
what mvregclean find you remove because the key is there but not the file ,folder or program.
even you reformat and it finds anything remove dont be afraid.
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I suggest you to use this free program to completely remove Winweb Security from your computer:
NVT Rogue Software and Trojan.FakeAlert Remover is a simple program that will help you to easily remove from your computer specific malicious software such as the Rogue Software, Trojan.FakeAlert and Trojan.Fraud.Load.
downloadhttp://www.novirusthanks.org/progs/11/
-How to use ?
1) Download
2) Open it
3) Click on “Scan your PC”
Go to your firewall antivirus website and search there to see if they have a fix for it or how to uninstall it. This sounds like that Antivirus 2009 my girlfriend picked up on the internet
try manual removal guide