Neptune is not visible without a telescope. It is one of the two more difficult planet to observe because of it's magnitude (brightness) in the night sky.
Because of it's distance from the sun less sunlight reaches Neptune. Because it's atmosphere is blue Neptune does not reflect a lot of the light that reaches it. Because it is far from Earth, the light reflected from Neptune does not reach the earth.
There are certain times in a planets orbit when a planet is “optimal for viewing.” For the outer planets: Mars, Saturn, Jupiter, Neptune, Uranus and Pluto the point of best viewing is at the Opposition.
Neptune can be found in the constellation Capricornus for the next few years. Neptune is at opposition around mid-September, so the best time to observe Neptune is between July and November.