The trick is to put the lens in your finger so that a Cup is formed. then hold the lens directly in front of your eyes so that you are looking to the side of the glass.
If the lens is a "U" with burned edges outside is inside out.Is only a "U", is in the correct position.
If you are using lenses with a tint of manipulation, another way is to put the lens in your fingertip and then looks down. the edge of a lens with tint should look very blue (or green, depending on the shade), it won't be the case if the lens is reversed.
Some also contact lenses have a laser marking, such as the name of the tag, the border to help you if you can read it correctly, the lens isn't inside out.
Don't worry if you put a contact lens in your eye inside out. the lens will feel uncomfortable, but it can't do any damage.