How Can someone prevent people from seeing what you are doing on the internet?

This answer must be prefaced with a warning: Any attempt to circumvent computer or internet policies at your employer's place of business may be grounds for immediate dismissal. Read your employee handbook for computer policies before continuing; and proceed only if it will not put your job at risk.

A key thing to remember is that the computer you use at your business is not yours; it belongs to your employer and anything you do on it is subject to his scrutiny and control. So, the only fully reliable way to prevent your company's network admins from seeing what sites you view is to use a different computer. To do that, you would set up your home computer to accept remote control requests, and then from your work computer, establish a remote control session with your home computer. You can then view whatever you want on your home computer, and the only thing the network admin will see is that you have opened a remote control link to your home computer.

Another user recommends "using the Windows program 'CCleaner' or try and delete your browser history and clear the browsers cache (if the IT people aren't too smart)"; against this it should be mentioned that all requests for web sites go through a firewall, and firewalls, particularly at larger corporations, will be set to log all requests. The record of where you've been browsing, and when, will be somewhere else entirely, and cleaning up your computer will only show that you knew you were doing something you shouldn't have been, and will get you into more hot water.