If you'd like some advice for fitting a new t(y)(i)re there's some great advice at:
http://www.bicyclinglife.com/HowTo/FixAFlat.htm
It covers a lot of stuff about fixing flats but goes through the basics of putting a tyre on. Depending on the tyre it could be quite tough.
However as long as you have one side of the tyre in first, partially inflate the tube to make sure it has it's shape, shove it in right around the rim, then starting about a 1/3 the way around from the valve squeeze with your fingers the tyre in on the opposite side bit by bit. It should be relatively easy until you have the last few inches left. Then you might need a bit of delicate brute force or maybe the very careful application of a tyre lever.
Before fully inflating go around the whole tyre squeezing the sides in making sure you didn't pinch the tube between the rim and the tyre... Then you're ready to go!
You could also get the bike shop the fit it while you watch and hopefully learn a thing or two.
It might turn out they sold you the wrong product
