What do I do to not show what I do on the internet?

[yahooligan]

Many browsers have settings that don't save browsing history. In Internet Explorer it's InPrivate Browsing. In Google Chrome it's InCognito. In Mozilla Firefox it's Private Browsing. Keep in mind that it won't save website history, etc etc on your computer. It will not protect you against people standing behind you, the NSA spying on you, or a duck somewhere in the world spying on you (anatidaephobia).
Make a habit of having legitimate things in tabs in a normal window, then have the "stuff that must not be named" in a separate window with the private/cognito browsing mode on. Therefore, if you parents come into your room, you can simply either "ALT-TAB" to switch to your previous window, or "ALT-F4" to close your "stuff that must not be named" window. Happy browsing!