I am resisting making a sarcastic comment about hiding your tracks after visiting porn sites, but, oh, there I went, saying it anyway. Okay, whatever. You visit what you want to visit, you look up whatever you want to look up, but remember that it's hard not to leave tracks on the Internet, as you're learning, hard to really be completely anonymous and not leave a trail behind you.

One thing you might want to consider is to learn a bit about what the Mozilla Firefox team refers to as "Private Browsing". The developers describe it thusly: "Firefox 3.5 and later provide "Private Browsing," which allows you to browse the Internet without Firefox retaining any of data about which sites and pages you have visited."

To use it, just look on the Tools menu:

Choose it and you'll get a confirmation:

Now you're good. Well, now you can avoid having your Web browser retain your history, at least. You still aren't anonymous on the Web, nor would your Google searches not be saved by the system automatically.

To accomplish what you're asking me about, clearing your search cache in Firefox for Mac OS X, you need to go somewhere else...

Before I go there, though, let me show what you're talking about.

You go to the Google search home page and see a nice empty box (and, if you're lucky, Bert and Ernie):

Type in a letter or two and suddenly:

Not so good if you don't want your search history overtly visible.

To fix it, on the same Tools menu, you need to choose "Clear Private Data..." (or, in the newer versions, "Clear Recent History"):

You'll get a helpful window with a variety of options:

At this point you can quickly delete everything that you've done for the last hour, or, if you click on that menu, you'll find more options for two hours, four hours, today and everything. Notice that you need to pick which caches you want erased too. To get rid of the Google search history, make sure you select "Form & Search History".

Click on "Clear Now" and you've removed your tracks. For now.

Good luck to you, hope this helps your exploration of the wild blue Web yonder.