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So that I could write intelligently, I checked my Big Blue Book of Bicycle Repair which my husband gave me. Unfortunately, it's all greek to me. So here goes with my first grade description.
I have a Specialized Dolce with 2 gears (front) rather than 3. I have a terrible time on hills and wonder if I can replace the 2 gears with 3.
Probably - but it will likely involve more than replacing the chain rings (front gears). You would likely have to replace the front derailleur and possibly the rear.
Other options might include keeping 2 on the front, but making the little one or both of them smaller - you might also be able to put a larger cassette on the rear. Both of these options might give you lower (easier) gears than you have now.
This is one of the questions that is best addressed by a competent bike mechanic IMO - who knows which parts go together and which don't.
You might have to replace the shifter and the chain, too, besides one or both derailleurs as Blueberry pointed out.
+1 on getting a mechanic to help you with the parts selection and do the installation. Drivetrain parts aren't necessarily interchangeable. Also +1 on at least considering a wider range cassette (which might still necessitate a new rear derailleur and definitely a new chain, but not all the other stuff).
Also may have to change out the bottom bracket. For what it's worth you really won't be gaining much in the way of extra gears going from a double to a triple (maybe only one or two.)
Whoops - I did forget to list the shifter, didn't I :) Just another reason to go to a mechanic:)