The starter is located on the lamp frame (there are typically two starters). When you turn on the light switch, the starter sends a jolt of electricity to the gas inside the fluorescent bulb. The ionized gas then conducts electricity and the bulb lights. When the starter stops working, the bulbs will either keep flickering without lighting or will only glow in the ends. (Flickering can also indicate the bulb needs replacing, but try the less expensive starter first.)
Replacing the starters is quick and easy—they simply twist in and out. Some starters are concealed under the bulbs, so they need to be removed first. A package of two starters only costs a few dollars. Bring the old one to the home center to be sure you buy the right replacement.
Most ballasts manufactured within the last 10 years or so don't need starters. Newer technology in electronic ballasts allows the lamps to light without them.