This whole process is actually surprisingly easy. With the App Store, Dropbox, and GitHub it only took me about 30 minutes to get my fresh OS X install up to speed and ready to work with all my applications, documents, and projects in place and ready to use.
I remember, back in the day, spending whole day doing a clean Windows install. I'm getting too old for that.
You're smart. I shouldn't even bother writing this section.
Create a Bootable USB Drive.
This step is not hard, and I've actually written another short post explaining exactly how to make a bootable USB drive.
However, @alecperkins reminded me that, starting with OS X Lion, you can use internet recovery instead of the USB drive. This is a nice option, but because OS X takes so long to download, it's sometimes not very practical. I like to keep a copy of the OS X bootable image on a hard disk somewhere so I don't need to download that monster any more than necessary.
Boot and Install
Once the bootable USB Drive has been minted, then plug it into the target machine for the clean OS X install and restart it. Hold down the option key for the entire time it boots until you see a new options splash screen.
It will give you several options for disks to boot from. Choose your USB drive, or you could also Choose Network for internet recovery. It will eventually give you another splash screen of options, of which you should choose the Disk Utility. Choose the target disk for the clean OS X install in the left pane of the Disk Utility. Then, with the target disk selected, choose the Erase tab, and then use Mac OS Extended (Journaled) as the Format type. Name the drive if you really feel like it.
Click the erase button. This is the point of no return. Everything. Is. Gone. Which is why you backed up your machine before you even got started down this rabbit hole.
But, hey, now it's ready for a clean, fresh OS X. Quit the DiskUtilty, which will dump you back to the main menu, where you can choose to Install Mac OS X. When given the option, choose your freshly erased and formatted harddrive as the installation destination.
When the reboot process is over, you'll have a clean install of OS X.