There are some easy steps you can take to enhance your privacy on the Web.
From the Safari menu bar, select
Safari ▹ Preferences... ▹ Extensions
Take an inventory of the extensions you've installed, if any. Some Safari extensions are adware or spyware. Read the privacy policies or terms of use carefully. Remove any that you don't really need or aren't sure about.
One extension that you may want to install is called "Ghostery." It blocks many tracking cookies. The extensions "ClickToFlash" and "ClickToPlugin" prevent Flash content from loading automatically.
If you've installed any ad-supported hacks such as "Glims" that modify Safari, uninstall them according to the developer's instructions. Doing so will enhance the stability of Safari, as well as your privacy.
In the Safari preferences dialog, select the Privacy tab. You have the option to remove data, such as cookies, stored on your computer by web servers. You can remove all such data, or remove only some of it by clicking the Details button. The other settings are pretty much self-explanatory.
On a more advanced level, you can change the DNS servers used by your computer, or your router, to look up the addresses of all Internet servers that you use. In general, the best choice from the standpoint of privacy is to use your ISP's DNS servers. Your Internet traffic goes through your ISP's network anyway, so in theory there's no loss of privacy in using its DNS servers. Avoid third-party DNS services such as "OpenDNS," which is in the business of selling information about you to marketers.
Consider using ad-blocking software such as "GlimmerBlocker," which also blocks some forms of JavaScript abuse that can be used to track you. It's only suitable for advanced users, and it may block some web content that you want to see.
This comment is not an endorsement of any third-party software. Do your own research before deciding whether to use such software.
When using a public network such as a Wi-Fi hotspot, keep in mind that others connected to the same network may be able to eavesdrop on your network traffic. They won't be able to read the contents of that traffic if you connect to secure websites such as this one, but they will know the addresses of the sites. The same goes for email and messaging. Some public VPN services market themselves as a solution to this problem, but using those services may have serious security and privacy implications.