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. 


This is a perennial question so I hope you will not mind me submitting another answer. The problem with the "table" approach is that it breaks the paragraph. This can cause spacing issues if your equation is part of a continuous sentence and your paragraphs have spacing before or after them. It also means that wrapping is done rather poorly for long equations (the usual preference in journals is that, if the equation is the width of the column, the number should appear below the equation right aligned instead of breaking the equation). Finally it does nothing to solve the problem that you wish to have punctuation marks instantly after your Display equation in the normal paragraph font. My solution is to insert a hidden paragraph break instantly after the equation. (With hidden characters showing, insert a normal paragraph break by pressing the return key, then select it and press ctrl+shift+H on a Mac, not sure of the Windows combination.) Then you may insert a tab and the appropriate equation number. When you hide hidden characters, the equation remains in the Display equation form, centred, but any additional text appears immediately after it on the same line. Another alternative is to insert a Style Separator in place of a hidden paragraph break. This accomplishes the same effect. However Style Separators are not available on the Macintosh edition of Word. Note this behaviour is undocumented and your equations sometimes become leftaligned instead of centred. I have yet to understand why. 

