How can I scroll horizontally with my regular mouse?

If your keyboard is near your mouse, you can hold the shift key down while you operate the scroll wheel. The window should scroll left and right.

Of course, the left and right arrow keys will scroll the contents of a window left or right in short steps.

Some mouse devices have additional controls and a software driver designed for Macs (Logitech, for example). Those drivers often add a settings pane to the System Preferences application that allow you to assign functions / keystrokes to those buttons. For example, a mouse I have used had a scroll wheel that you could move left or right, activating a separate switch in each of those two directions. Using the settings pane, I was able to set the driver to scroll left or right by activating the left-right function of the wheel.

If your mouse has a middle click (scroll wheel that you can click, for example), you should be able to click it to enable auto-scroll. On sites with horizontal scroll area, the auto-scroll should allow you to move the cursor left or right to scroll in that direction.

More info: The Many Things You Can Do with a Middle Click on Your Mouse