Create a USB Boot disk for MAC

Why do you need a bootable USB drive

If you only use Apple software and hardware, you will not need this. But if you want to replace your hard drive, this can come in very handy.

How to do it in 3 easy steps

Open Terminal.app

The easiest way is to press Cmd+Space, then type "Terminal" and press "Enter".
Before you press "Enter", it should look something like this:
After pressing "Enter" you will have a terminal, like this:
The text in this screen will not match yours, this is not important.

Do some magic

In the Terminal, past the line: defaults write com.apple.DiskUtility DUDebugMenuEnabled 1
It should now look like:
If it does, press "Enter". Then Quit the terminal.

Open Disk Utility.app

Press Cmd+Space, type "Disk Utility", then press "Enter".

Show all partitions

From the "Debug" menu select "Show every partition".

Select "Recovery HD" from the left menu

Select the "Restore" tab

Drag your USB drive into the "Destination:" field

Your screen should now show something like this:
If so, press "Restore".

Erase the USB drive

A warning will appear, consider carefully if you want to overwrite the drive, and press "Erase".

There is no step 3

You've just created a Mac OS Recovery USB drive.

How to use it

Just reboot by opening the apple menu, and selecting "Restart..." (or whatever your localisation my be). Then, while booting, hold the alt (option) key. There will be a boot-drive selection screen, select your USB drive.

After booting; you will be able to recover from a backup, install a fresh system, run the Disk Utility to recover file system errors, etc.

Other ways

There are a few ways to create a boot disk for MAC. Generally, they are pretty complicated and require the "Install OS X Mountain Lion" app to be available. The "Install OS X Mountain Lion" app is not present in all Mac's.