Can also be used to "fresh install" Mavericks in case of software or bad sector issues/glitches
If your having problems with Mavericks, and you want to keep it, you should first try to fix in place: ..Step by Step to fix your Mac
If you can't do any of the following, then let a professional assist you before you delete your data!
How to remove OS X 10.9 Mavericks and restore your previous operating system version
1: While in OS X Mavericks, you will need to manually (no TimeMachine) backup all your user files to a regular external drive formatted Applications/Disk Utility > Partition 1, click the box, Option: GUID and Format OS X Extended Journaled and give it a name and click Apply. Formatting a drive will erase all pre-existing data on the drive!
2: Manually drag and drop copy each user folder of Music, Pictures, Movies, Music, Documents etc., into new User named folder on the external drive. Make sure to export bookmarks, grab email addresses, address book data and and product license keys etc., data that's not in your users files.
Preinstalled purchased software when the machine was purchased new may not be restored to the machine. Extra steps are required by contacting Apple or downloading from AppStore. For instance the free iLife that comes with the machine can be restored via AppStore easily. Versions grandfathered in from Snow Leopard (or earlier) will have to be reinstalled when Snow Leopard is before upgrading.
Copy (but don't restore) the User/Library folder or the entire User home folder as in 10.7+ it contains a hidden User/Library that changes with OS X upgrades and can't be used in the earlier OS X versions. So avoid restoring it to the previous OS X version until more is known if any of that data can be accessed/recovered.
Only copy user files folders of (Music, Pictures, Movies, Documents etc in visible folders) should be restored to the previous operating system. iPhoto Library is a package, right or control key click on it to "show package contents" the Originals or Masters folder contains your original pictures. Ditto for any other proprietary packages which may not work in older versions of software on the older OS X version.
The longer one takes to revert from a later OS X version, the harder it is to do so because of changes to software support files containing your work etc.
So if you just upgraded to Maveriks and want to revert, good chance your programs haven't updated their support files yet.
OS X, programs and user accounts/Library will be restored brand new and upgraded. Unfortunately erasing everything is the only way to revert to a earlier OS X version as the RecoveryHD partition either has to be erased or reset to the earlier OS X version, along with the EFI and GUID partition map in the case of Snow Leopard reverts.
Write down the user account names for later restoring.
To ensure the iTunes and other databases work, the pathnames to your music and other files must match. This is optional, the song files can be tagged with the playlists they are in (attaches to the song files themselves) and the iTunes database file edited in TextEdit to alter the pathnames accordingly.
There will be more work involved later if you do change the names on the user accounts different than the files they came from. Some people opt for this after finding out OS X puts their real name all over the machine and broadcasts it via Bonjour/emails, I understand the security risks.
3: If you have BootCamp, you need to boot into Windows and back that data up also. Use Winclone 3 in OS X to also clone the BootCamp partition for later restoring.
4: Make sure to have at least TWO copies of your users data on two separate pieces of hardware at all times. Mistakes occur and your going to pray you have another backup of your precious files. Label all drives so your sure what is what during this confusing time. Unmount and disconnect all non-essential hardware, including the backup drives.
5: Be near your fast, reliable Wifi, or physically connect your Ethernet cable to the router or modem (off/on to reset). Have your AppleID and passwords available, have your email address available. Have your Wifi password available. Connect your machine to power if it's a portable model. You will need a wired or built in keyboard for the at boot key commands.
6: Once your sure, we will begin. There are basically two sorts of Mac's that can be restored. Those that have Internet Recovery and those who don't.
Reboot the machine while holding command option and r keys down on a wired or built in keyboard to check if Internet Recovery loads, a globe appears.
Those who don't have Internet Recovery will have to revert to using the Snow Leopard retail (10.6.3) or gray 10.6+ disks that came with the machine. Do not use 10.4 or 10.5 disks. Do not use disks from another model of Mac. The 10.6.3 white retail "upgrade" disks have the full OS X 10.6 on it (sans the free iLife). If you lack these disks, call Apple with your serial number or model identifier you can gleam from System Profiler in your Utilities folder.
If you want to make a bootable clone of Mavericks, now is the time to do it. How to clone your boot drive
It is IMPORTANT that the ENTIRE boot drive be completely erased to restore the previous OS X version onto the machine.
(This will include erasing Boocamp, EFI, RecoveryHD and the MacintoshHD partition containing your OS X, programs and user accounts/files.)
A: Snow Leopard (10.6) reverts.
Follow this User Tip and select the drive makers name and size at the top in Disk Utility. Then setup and Software Update to 10.6.8, then log into AppStore and upgrade to your last OS X version you desire by holding option key down and clicking on Purchases section of the AppStore.
Also read this for preparing your files for returning to Snow Leopard.
Restore your free iLife before further upgrades of OS X: Restoring your Free iLife (iPhoto, iMovie etc)
B: Internet Recovery returns for 10.7-10.8.
Hold the command option and r keys down on a wired or built in keyboard. Boot the machine and you will see a globe spinning as IR loads.
Next select Disk Utility and the disk0. Click Erase and if there is a slider, move it one or two spots to the right for a 0-3x secure erase and mapping off of bad/damaged sectors on the boot hard drive (SSD no need).
Once finished, check Partition that Option:GUID and Format is OS X Extended Journaled and the name is MacintoshHD or else make it so and click Apply.
Quit and install the OS X version that is provided with Internet Recovery, it depends upon what originally came on the machine.
7: After OS X is reinstalled. Upgrade to the version you want from the Purchases section of the AppStore. Or restore from a TimeMachine drive that predated the OS X upgrade or from your bootable clone made with Carbon Copy Cloner (as it also copies the RecoveryHD partition, SuperDuper does not.)
Install your programs from original sources and create new accounts and transfer the files back from the external storage drive if applicable (reverting or fresh install method)
Restore your free iLife: Restoring your Free iLife (iPhoto, iMovie etc)
8: Restoring user accounts: Set up new accounts with the same name as before, then move the CONTENTS of the backed up users folders into their respective new folders on the new accounts. It's important for iTunes, other databases etc., that contain pathnames to your music and other files be preserved. This is optional of course, ut you will have more work restoring playlists and such. However if one took precautions and tagged songs in the playlists wih the name of the playlist, then tagged songs can be rebuilt into new smart playlists.
iPhoto Library and others like it (Aperture databases) are actually folders, simply right or control/alt key click on them and "Show Package Contents" inside is folders containing the originals.
Odds and ends
IF YOU HAVE A THIRD PARTY SSD: You will need to re-enable TRIM by using third party software on MacUpdate.com
If you've installed NTFS format reading software, reinstall it obviously and any other essential software from original sources so it's pristine.
Remember 10.8 users and above have to right or option/alt key click on a lot of software downloaded from the Internet to get past OS X "Gatekeeper".
If you have a problem with User Permissions on the returned files, see #6 here and apply.
See more of my User Tips in this section
Edit: An alternative to these steps is to use Snow Leopard Server in a Virtualized environment.