Warning: there is no way to completely cover your movements online.
The only way to ensure privacy is to use a different computer, such as in a local library or at a friends house. You don't have to be a computer expert to track someone's movements online.
As a rule, internet browsers will save certain information as you surf the internet. This includes images from websites visited, words entered into search engines and a trail ('history') that reveals the sites you have visited. Below are instructions on how to minimize the chances of someone finding out that you have visited this website.
If you do not use a password to log on to your computer, someone else will be able to access your email and track your internet usage. The safest way to find information on the internet, would be at a local library, a friend's house, or at work.