New to biking and just bought a 2005 Dolce

[Owlie]

Ooh, pretty blue and silver. It looks like you have the same "trigger" set-up that I do.

For the rear set of gears, smaller gears (the ones further from the body of the bike) make it harder. These are good for going really fast. Pushing that "trigger" shifter on the inside of the right brake hood will shift the chain onto a smaller gear than the one you started in. If you ride with your hands on the hoods (the spot where you're in easy reach of the brakes), just press it with your thumb. To make it easier, you shift to larger gears (closer to the body of the bike). For that, the right brake lever (silver) actually acts as your shifter. Push the brake lever toward the center of the bars. Tada!

For the front (chainrings), smaller (closer to the frame) is easier. Press the thumb-trigger thing on the inside of the left hood to get there. Larger chainrings are harder (again, good for going fast). Push the silver lever in toward the center to shift.
(Unless its previous owner had it set up very strangely...If that's the case, you could probably take it to a bike shop and have them switch the shifter cables around so that it's a normal set-up.)

Find an empty parking lot and just play around with the gears a little.