Please refer to macOS Sierra: Revert to a previous macOS version.
Assuming you have no Time Machine or equivalent backup of your essential files and other documents, create one now because you will need to completely erase that Mac in order to downgrade its operating system from Sierra to any earlier version. To learn how to use Time Machine read Use Time Machine to back up or restore your Mac.
After you have that backup and are satisfied with your ability to recover its files — or you decide that you do not need or want any of the information on that Mac, and understand that it will be irretrievably and forever lost, continue with the steps below.
- Shut down your Mac, and restart it using macOS Internet Recovery.
- Read the * note to determine how to force Internet Recovery.
- You will need a viable Internet connection, preferably a fast one, and one that does not require a "login screen" for you to connect to the Internet.
- If you do not boot Internet Recovery, you will boot into the existing Recovery Partition, which will only allow you to reinstall your existing operating system.
- Then, select Disk Utility to completely erase your startup volume.
Choose one of the Mac OS Extended (Journaled) formats.
- Then, select Reinstall OS X.
- That reinstalls the operating system installed on your Mac when it was new.
- It will not require an Apple ID to install.
- If you are prompted for an Apple ID before it even begins to install, return to Step 1.
- Install that version of OS X, following its instructions.
That is where you will be prompted for an Apple ID (although you can skip that step if you choose).
- Finally, download and install the operating system you wish to install from the Mac App Store's Purchased page.
- If that is El Capitan, you can use this link: Get El Capitan from the App Store.
Then, restore your files from the backup. Beware that if any of them have been updated to work with Sierra, they may no longer work with El Capitan or earlier OS X versions.
Lastly, you would be far better off fixing what's wrong with your Mac than to downgrade to an earlier operating system. If you want to do that, and I strongly suggest you do, please write back for instructions.