On a Hanukkah menorah, the helper candle is kindled first, and then it is used to light the candles for that night. Among the Hanukkah candles themselves, the newest candle added for that night is always the first one lit.
Shamash (helper candle)
The shamash, usually raised or set apart in the center or on the side, is lit before any of the other candles. It is then used to light the rest, since the eight main candles are reserved only for the mitzvah and not for practical use.
First night placement
On the first night, one candle is placed in the far-right holder of the menorah (as you face it) and is lit using the shamash. That rightmost candle is the only Hanukkah candle lit that night, after the shamash.
Order on later nights
Candles are added from right to left as the nights progress, but they are lit from left to right. This means the newest candle—the one furthest to the left for that night—is always lit first with the shamash, followed by the others in order toward the right.
