There are so many ways of people seeing what you're doing it's not even funny. Basically there's no way to guarentee privacy, but there are things you can do to reduce the chances.
P) Someone walks up behind you and looks at the screem.
S) If you don't want someone to watch what you're doing, make sure you're in a private place. You can also purchase screen shields, which prevents the viewing of the screen beyond a certain distance.
P) Someone can install spyware onto your computer to monitor everything you do, and even record keystrokes and take screenshots.
S) Make sure you use a firewall, antivirus, and spyware protection, perform regular sweeps, and be ensure that only select people can sign onto your computer by using password protection. Software availability and methods of securing your PC depend on your OS. Just be aware that some spy software can avoid detection, so there's no guarentees.
P) Your browser history, cookies, cache, autocomplete, etc, as well as MRU (most recently used) file lists all tell where you've been.
S) There are various methods and rograms for clearing such information, but it depends on what browser and operating system you use. Again, nothing's perfect, so traces will always be left behind.
P) Your communications over the internet can be intercepted by hackers.
S) Watch what personal information you give online, try to stick to secure sites/transmissions, and be aware of sites that imitate legitimate ones. You can also use proxy servers to help prevent people from identifying/locating you.
P) Your ISP can, of course, can keep track of all communication that occurrs over their network.
S) Frankly, there's nothing you can do about that. Just hope they follow the laws and their own privacy policies (if applicable) and don't go snooping.
And, of course, if you really don't want anyone to find out you did something, don't do it in the first place. You don't have to worry about hiding something if you have nothing to hide.
Hope this helps,
P.S. You'll need to provide more information if you want more definitive answers/solutions.
how do i keep others from seeing what i look at on the internet?