How do you delete your browser history?

In Chrome, Mozilla or Explorer you can go to the icon on the top right. You can then click on history and clear.

A word of caution though - you will not succeed in removing ALL traces of what you have been up to on your computer unless you completely overwrite the entire disk. Barring that, a good computer forensic examiner will still be able to recover all sorts of artifacts that will show so much that it won't much matter if you delete your history or not. Deleting your history only prevents a casual examiner from seeing where you have been.