Double Exposure involves the overlay of an image over the top of an existing one, while being able to see both the overlay and original.
In order to achieve this you can use two techniques:
Camera:
Most cameras come with a double exposure mode, allowing for two or more photos to be taken over the top of each other within the camera itself.
Photoshop:
By duplicating or adding in another layer over the top of the existing image and altering the opacity then moving the image to create the effects demonstrated below.
For this experiment, I decided to alter the hue of separate layers in some instances to give off a trippy effect