Hi Brian,
Unless you have a Yosemite recovery partition on your hard drive, Apple will do their best to appear to be helping you, but it will fail for multiple reasons each time. So here is my solution (assuming that you don't run Boot Camp) to your requirements:-
1. Use Disk Utility to partition your hard drive. This is easy, straightforward and almost self-explanatory.
You should protect your data by backing it up to an external drive before doing this unless you are already fully
familiar with Drive Utility because it is possible to make it all disappear in an instant !
A great way to protect all of it, including the operating system itself, is to use Carbon Copy Cloner (CCC)
which can be used for FREE. The 'trial' can simply be installed again and again as wanted. There are many other
cloning and backup applications, but this one is great and is free. Works right 'out of the box'.
N.B. If you find it useful to the extent of using it frequently, then pay the man for his work.
2. Find a friend running Yosemite and ask if you can clone their hard drive onto an external drive.
Again using CCC, clone their drive. You can then reboot their machine from the clone and proceed to eliminate
their private data from it. Delete the desktop, Downloads, Documents, email accounts, browsing history etc.
You could also uninstall any software they have added.
3. Open System Preferences and go to Users & Groups. Add yourself as an administrator and then highlight your
friend's name and press the minus at the lower left of the window. It may tell you that a reboot is needed to
complete that action. Reboot and you should now 'own' that installation ... remember we are still on the external
clone, NOT the internal drive.
NOTE: In case you are unsure of how to be certain you are on the correct drive, either,
a. set the external drive to be the Startup Drive (in System Preferences), or
b. boot with the ALT key held down until some pictures of drives appear, yellowish ones are external.
Unless you gave the clone drive a name, it will be called Untitled.
4. Reboot the machine using the INTERNAL drive this time. Go to System Preferences and reset the Startup
Drive to be the internal drive. It may already be set, but check it rather than leave a problem.
5. Connect the clone drive to your machine. Boot whilst holding down the ALT key as we did above. This time you
will see your clone drive and it's Recovery Volume. Boot from the Recovery Volume. This will allow you to reinstall
Yosemite without keeping files .. i.e., a CLEAN install.
6. Once all of that is completed and checked, use CCC to clone your new system to an external drive. That covers
you if you ever want to do it again. Now you should delete anything that remains of the clone from your friend's
machine ... mostly as a matter of respecting their privacy and possibly Apple's copyrights. I assume here that you
have or had a right to run Yosemite before you moved to El Capitan, otherwise it might not be legitimate to do
what I have described here.
7. Lastly, you can use Disk Utility to shrink the volume containing your freshly made external clone so that you make
more drive space available for making another clone on another partition after you install all your software, email
accounts, etc.
I hope this solves the problem for you and anyone else struggling with the same or similar issues. You will be expert with Disk Utility, Users & Groups and CCC by the time you are done. Allow about an hour-and-a-half to clone your friend's machine and another hour to do all the cleanup and changing administrator etc. Back on your own machine, the time will be the install time which is as much down to Apple's servers as anything else. The further cloning that I recommend will also take time and I suggest just letting the machine get on with it. I set mine so that it never sleeps or runs screen savers when I run CCC and I don't use it for anything else whilst cloning.
Let me know if I can help further, or if anyone spots an error in what I have written .. it is all from memory !
Good Luck,
David