Avoid data trails on the internet: Mozilla Firefox

You may do settings for firefox manually or use a plugin.

Manually

Open Options in Menu Tools.

Plugin: Using PrefBar

If you want to use PrefBar to manage these settings comfortably, please read this this guide.

Note: These are basic settings. Using a filter proxy will offer more options for blocking content.
Cookie Culler is a plugin which allows deletion of unwanted cookies while keeping wanted cookies.

Test: Test these settings for anonymity using this guide.