How do I downgrade from Yosemite 10.10 to Mavericks 10.9?
Backup Mavericks using Time Machine first (if possible)
  
  Follow these steps to get a copy of Mac OS X Mavericks:
  
  
  Open the App Store.
  Enter your Apple ID and Password and click Sign In (if App Store requests it).
  Click Purchases.
  Scroll down to find Mavericks.
  Click Download.
  
  
  Now that you have downloaded the Mavericks file you will find it inside Applications.
  Revert to Mavericks by creating a Mac OS X USB boot drive.
  
  How to make a bootable Mavericks install drive
  
  You can use this file to turn an 8GB USB Flash into a Mac OS X Mavericks boot drive. With this USB Boot Drive you can wipe the hard drive on your Mac, and install a fresh copy of Mac OS X Mavericks. If you have your Mavericks Time Machine backup, it can be used to reinstall all your files and programs (otherwise you’ll need to setup your Mac from scratch using the files you backed up to an external drive or cloud storage solution).
  
  Using a Mac OS X Mavericks boot drive to perform a fresh Mac OS X installation
  
  
  Shut down your Mac (Choose Apple > Shut Down).
  Insert the Mavericks USB Flash Drive into your Mac.
  Startup the Mac while holding down the Alt key.
  Choose the USB Flash Drive Volume.
  Choose Utilities > Disk Utility on the Install Mac OS X window.
  Select your main Volume in the sidebar. Now click Erase > Erase (warning, this removes everything on the volume).
  Click Disk Utility > Quit Disk Utility.
  Tap Continue on the Install OS X window.
  


Check out this MacWorld article. It explains each step in detail.

Note: In some rare instances, it may be necessary to format the Macintosh HD partition before installing Mavericks. **This will erase your entire hard drive ** so be sure to back up any files you need before going this route. I've outlined the steps to do this below:

1.) Boot the Mac from the USB you made using the steps above. 
2.) Open Disk Utility and erase the drive entitled (Usually) "Macintosh HD". You can rename it whatever you like. 
3.) Install Mavericks.