The shamrocks you're likely to find in gift shops are variants of oxalis, or wood sorrel, grown from bulbs that occasionally go dormant or "need to rest." If it's been properly cared for, your shamrock plant may keep flowering all winter long, going dormant only during the summer. If its foliage is healthy but the plant refuses to flower, you may need to allow it to go dormant for some time, after which it should once again flower reliably.
Place your shamrock plant in a bright, sunny window during the winter. It requires direct sun, and will flourish in the cooler temperatures usually offered by proximity to the window.
Keep the soil in your shamrock plant barely moist; test it with your finger and water it moderately just as the soil begins to feel dry.
Fertilize your shamrock plant every two weeks during the active growing phase. Use a half-strength, balanced houseplant fertilizer.
Watch for the shamrock's leaves to start dying back once temperatures warm into the 70s, or summer approaches. When this happens, either cut the leaves back to soil level, or let them die off naturally; the plant is not really dying, but going dormant. Stop watering and fertilizing the shamrock during this process.
Place the shamrock in a cool, dark place, like a covered container in the garage, for two or three months. After about two months, check for signs of new foliage poking out of the soil every week. This foliage is your signal to place the plant back in its sunny window and start watering and fertilizing again.