How can one determine whether a tea set is sterling silver or silver
plated?  the only identifying factor to this layman is that the set
was manufactured in India.  Any help out there?

Calculate the density of the silver. 

Fill a bucket up with water to the top, place the silver in the bucket
and measure the volume of the overflow water.

Then weigh the silver. 

Divide the weight by the volume and you will get the density.
http://www.allmeasures.com/Formulae/static/formulae/density/29.htm
Will allow you to easily input your mass and volume in the units you
measured them in.

Pure silver is around 10.5 grams per centimeter cubed

That is, the silver (if such) should be about ten times as heavy as
the volume of water displaced, or not much less.
Is the tea service apparently old?  Is it carved or engraved?  Search
for signs that plating has been worn through on the bottom edges of
the pieces or from polishing.  Take it to a store that sells such and
compare the weight.  Testing the silver may tell something. 
Electroplated items are plated with 100% silver, but sterling (92.5%)
is less and, of course, an even lower silver content would indicated
that it is not plated.  If it comes from India, it is probably not
Sheffield plate, a different process of applying silver to a base
metal, whereby the silver would not have to be 100%.
IF it is old, there is a pretty good chance that it is not plated, but
the silver content could be well below that of sterling.
I hope the set is attractive.  That is the most important factor for
your enjoyment.
Good luck, Myoarin