How do I format new Samsung 850 Pro SSD in my 2012 Mac Mini

Question

So my 12 year old is frustrated by the slower speed of his mac mini, and with some of his birthday money and my expertise (which I hope to borrow from you and pass off as my own), I've purchased a Samsung 850 Pro SSD (256 GB) and am going to install it for him.  We've already increased the memory.   I've also purchased the OWC data doubler and am planning to install the Samsung with the original Mac hard drive.  
Having watched the install videos several times I feel fairly competent to do that, but my question is what to do then to access and make the most use of the SSD so everything (1) works and (2) runs as fast as possible?    For example, first, do I need to copy the OS to the SSD and delete from the Mac hard drive, and then somehow set up the SSD as the main drive?   And do I do this before I install the SSD or can I do it after?   Finally, what do I need to do to ensure that the computer uses the two drives optimally thereafter for maximum speed/performance.  You can see my level of expertise from my questions.
Other than the memory and the SSD install, we're not planning any other modifications, and his use of the mini is pretty vanilla (games, videos, etc.).    Any step-by-step help for a relative novice in this area (me) would be much appreciated.   
My Mac's specs:
Mac mini (late 2012)
Processor:  2.5 GHz Intel Core i5
Memory 16 GB
OS X Yosemite (10.10.2)

Answer 1

1. Partition and format the SSD.
2. Install OS X on the SSD.
Install OS X Using Internet Recovery
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
Boot to the Internet Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND-OPTION- R keys until a globe appears on the screen. Wait patiently - 15-20 minutes - until the Recovery main menu appears.
Partition and Format the hard drive:
Select Disk Utility from the main menu and click on the Continue button.
After DU loads select your newly installed hard drive (this is the entry with the mfgr.'s ID and size) from the left side list. Click on the Partition tab in the DU main window.
Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Click on the Options button, set the partition scheme to GUID then click on the OK button. Set the format type to Mac OS Extended (Journaled.) Click on the Partition button and wait until the process has completed. Quit DU and return to the main menu.
Reinstall OS X: Select Reinstall OS X and click on the Install button. Be sure to select the correct drive to use if you have more than one.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.
This should restore the version of OS X originally pre-installed on the computer.
How to use an SSD with your HDD
If you are going to use an SSD as a boot drive together with your existing HDD as the "data" drive, here's what you can do.
After installing the SSD you will need to partition and format the SSD using Disk Utility. Then, install OS X on the SSD. After OS X has been installed boot from the SSD. Use Startup Disk preferences to set the SSD as the startup volume.
Open Users & Groups preferences. Click on the lock icon and authenticate. CTRL- or RIGHT-click on your user account listing in the sidebar and select Advanced Options from the context menu. You will see a field labeled "Home dir:" At the right end you will see a Change button. Click on it. In the file dialog locate the Home folder now located on the HDD (HDD/Users/account_name/.) Select the folder, click on Open button. Restart the computer as directed. When the computer boots up it will now be using the Home folder located on the HDD.
Another more technical method involving the Terminal and aliases is discussed in depth here: Using OS X with an SSD plus HDD setup - Matt Gemmell. This is my preferred approach because I can select which of the Home's folders I want on the HDD and which I don't want. For example, I like to keep the Documents and Library folders on the SSD because I access their content frequently.
Be sure you retain the fully bootable system on your HDD in case you ever need it.