Dual Boot Mavericks + El Capitan

Solution 1:

What you need to do is to create another partition on your Mac, and install Mavericks on it:

1. On your El Capitan partition, open Disk Utility (in Utilities) and select the physical hard drive in your Mac. It should be titled "APPLE HDD ... MEDIA" or something similar:
2. Click "Partition" and click the "+" sign at the bottom of the pie-chart hard drive. Select how big you want the new partition to be and give it a name:
3. Make sure the format is "OS X Extended (Journaled)" and click "Apply". It may take a few minutes to create your new partition.
4. Next, you will need to obtain a copy of the OS X Mavericks installer. If you have previously downloaded it, you can redownload it from the "Purchased" page in the Mac App Store, you could download it from a friend's computer (if he has purchased OS X Mavericks), or if you are on a paid Apple developer account subscription you could download a build on the ADC Downloads page.

If you have the Mavericks version of Internet Recovery, as you said you might, you can boot into it by holding Command-N at startup and clicking "Reinstall OS X Mavericks", and skip to step 10 and onwards. However, it is possible that with an OS X upgrade the process upgraded your version of Internet Recovery to the El Capitan version, for example.

5. Once you have the OS X Mavericks installer, you should copy it to a USB thumb drive. Copy the installer onto the thumb drive by dragging-and-dropping in the Finder.
6. Leave the USB drive in your computer with the Mavericks installer.
7. Shut down your Mac.
8. Hold the "option" key while turning your Mac on. You can release the "option" key until you see the Apple logo.
9. You will be presented with icons of your hard drives and external drives. Use the arrow keys to select the USB drive you made with the Mavericks installer on it and press the "Enter" key.
10. Go through the Mavericks installer process. When prompted for which disk you want to install Mavericks on, choose the new partition you created in Disk Utility.
11. The Mavericks installer will copy over all the files needed, and restart as part of the process.
12. You will be taken through initial setup of your "new computer" and when it is finished you will be using OS X Mavericks on a partition of the hard drive.
13. You can select which OS to boot into at startup by holding the "option" key while turning it on until you see the Apple logo. Use the arrow keys to select which partition.
14. You can set your default startup disk (i.e. what disk the computer automatically boots into without having to hold the "option" key) in System Preferences > Startup Disk.

Solution 2:

An alternate approach, if you haven't already upgraded, is to use CarbonCopyCloner to make a full bootable backup of your hard drive before upgrading.

You can even make the backup, boot from the external drive, and then upgrade that installation instead of upgrading the OS that's directly on your computer. Then play around with the upgrade before you fully commit to it.

I used CCC successfully to partition up an external hard drive and install multiple Mac OSes on it, so that I could boot my computer from Snow Leopard, Lion, Mountain Lion or Mavericks.

And of course you should have a full backup of your computer anyway, even if you don't need to boot to a different Mac OS.

I'm not affiliated with CCC, but I think it's awesome and every Mac power user should be using it. :)