Why is Neptune blue?
Short answer: Methane in Neptune's atmosphere absorbs red light and reflects blue light.
Long answer: Neptune's atmosphere is made up of hydrogen (80%), helium (19%) and methane (1%). Despite only being a small fraction of the overall atmospheric composition, methane in the upper atmosphere is responsible for Neptune's blue colour. Methane absorbs the red part of the light from the sun and reflects the blue light. This makes Neptune look blue.
When you look at Neptune you're seeing reflected sunlight, with the red part of the spectrum missing and the blue part still there.
Image credit: NASA, Voyager 2 robotic probe, August 1989.