If this has happened to you, go to the 'Report an Incident' page and log as much information as possible. The more information you can provide, the more chance we have of raising awareness.
If you live in the UK, the Police recently launched an initiative called 'Action Fraud' who will be able to take down your information a log a case for you. Call the number below:
If you live in the US, you can log your incident with iC3 (Internet Crime Complaint Centre)
If you think you may have given your credit card information to a scammer, the best advice would be to contact your bank and report it as soon as possible.
An operative supposedly calling on behalf of Microsoft calls and asks to speak to the main PC user in the house. The caller then claims that he/she has been given information that your computer is behaving strangely, running slow or might be under the influence of 'malware'.
The caller talks you through opening a program on the computer called 'Windows Event Viewer' or 'eventvwr.exe'. Once there, you are shown the Application Log which typically has quite a few 'Warnings' or 'Errors'. These are nothing to worry about, and simply report tiny abnormalities in your system which require no action.
The caller tells you that these warnings and errors need fixing urgently and attempt to direct you to their website, either www.teamviewer.com or www.logmein123.com or www.ammyy.com in order to initiate remote control of your computer. Once they have control, they have access to files on your computer than can potentially contain sensitive information. They are then free to infect your computer with whatever malware/trojans/malicious software they wish. Chances are, they will then try to charge you a 'Service Fee'.
NEVER allow unsolicited remote control of your computer, and
NEVER EVER allow yourself to get talked into giving your credit card or bank details.