Browers like Netscape and Internet Explorer are designed to leave traces behind indicating where you've been and what you've been looking at on the Internet. It's hard to absolutely guarantee that your travels on the Internet can't be traced at all, but here are some simple things you can do to reduce the chances that someone can look through your computer and find out what you've been reading.

In general you need to erase two different things after you've left any other site that you don't want traced.

History/Cache File
If an abuser knows how to read your computer's history or cache file (automatically saved web pages and graphics), they may be able to see information you have viewed recently on the internet.

Netscape  
Pull down EDIT menu, select PREFERENCES.  Click on ADVANCED, then choose CACHE. A screen will appear where you can click on the buttons, "Clear Memory Cache" and "Clear Disk Cache." Click on each of these and then hit "OK." Your cache will now be cleared.
      

Click on the EDIT menu, choose PREFERNCES, then choose NAVIGATOR. A "Clear History" button will appear on the screen. Select it, then choose "OK." Your history list will now be erased.
       

If you've got a more recent version of Netscape installed on your computer, you will also want to clear your location bar list. Open the EDIT menu, choose PREFERENCES, then choose NAVIGATOR. Click on "Clear Location Bar" button at the bottom of the window, then choose "OK."

Internet Explorer
Open the VIEW menu, choose INTERNET OPTIONS, then choose the GENERAL tab at the top. In the section called "Temporary Internet Files," click on "Delete Files" to clear your cache. On the same screen, in the section called "History," click on the "Clear History" button to erase your history list.  In Interent Explorer, clearing the cache and history will automatically clear the address bar on your browser.

One Additional Tip
When you clear the cache and the history list, you erase not only the information on where you've been, but any other information that had been previously stored there. So, if your partner checks and sees that the cache and the history list have been completely emptied, they'll not only know that you know how to do this, but they might guess that you're trying to hide something. One possible way to avoid suspicioin is to clear the cache and history once you're done looking at information you don't want your partner to know about. After they're cleared, spend some time visiting sites that you think your partner wouldn't object to. This way, the cache and history list start to get filled up and your partner might be less likely to notice that old information is missing.