There are many different methods to getting rid of a unibrow. A few go the easy route and make a quick swipe with the razor when shaving. Don't do that. While the hair won't grow back fuller as the old wives' tale might suggest, it will grow back with blunt ends, which looks thicker. Plucking is the easiest, cheapest and least painful solution.
You'll want to pluck right after a warm shower, when your pores are open and the hair has softened.
Turn the sink on to the hottest water you can stand. Wet part of the towel and hold it onto your brow for about a minute. To really see what you're working with, get a mirror with at least 5x or 10x magnification.
For optimal results, use a slant tip tweezer, like the pair shown below. Start tweezing in the middle of your eyebrow region, working your way towards the part of your eyebrows that you want to keep. Make sure you stretch the skin with your free hand as you go.
If you want to thin your individual eyebrows, start from the bottom and move upwards while keeping the shape of your brows. When finished plucking, turn on the cold water. Put a small section of the hand towel under the water for a few minutes. Place it on the plucked part until the towel no longer feels cold. The cool temperature and pressure closes the pores on the tweezed area.
You can also wax your unibrow, but get it done by a professional.