How do you create equations in Word 2010 that are automatically numbered with the equation number centered vertically on the equation and right justified? While a number of references have discussed the use of three column tables, finding a step by step proceedure kicked my but for some time.

You can create a template that can be used to automatically generate the table and equation with number to the right:
Now if you want to insert an equation with automatic numbering in standard journal/conference paper format, just select the template you have made from the equation gallery and it will insert it into the document as desired. Equation numbers will be automatically updated and references can be made to them using the References > Cross Reference option for equations. NOTE: If you'd like to save this newly formatted equation as a keyboard shortcut (like pressing the Alt and + keys simultaneously in order to create a new equation), you can do so by going to File > Options > Customize Ribbon > Customize Shortcuts and then selecting "Building Blocks". 


Personaly, I use the method as described in the answer of @R Schultz. But if you are specifically looking for a tool to do it, look at Kutools. Here they also describe an alternative way to insert model numbers without using their tool. I have not used Kutools, so no idea how well it functions. 


I usually just press TAB (the same number of times on both sides of the equation) until the number is at the righmost position. 


Microsoft already answered your question: you may find an extensive tutorial dedicated to equations in this article:
There are several solutions posted there, for both left, center and rightside numbering and even a samble VBA solution. It's a little bit old, true, but basics never changed that much over the years. You can also read through a less specific, but more uptodate and illustrated caption tutorial. It is a general tutorial, but applies pretty well to equations  especially in pair with the KB article. 

