Since photography is usually considered to be an interpretation of reality, you do not always have to break that relationship with the viewer and can instead integrate elements of the surreal experience into a realistic photo. This can be done by breaking the expectations for how a location, or object, would be represented in regular sight. You can hyper expose the image, under expose the image, increase contrast to a normally objectionable point, or even alter the relationships between the colors. All of these are fairly easily achievable principles used either in the production of images or through photo editing, but change the balance of sight that is common.
If you want to begin utilizing this representation when in your photo production you should begin in much the same way as you would with abstract photography and use your camera less as a normal tool for image capture and more as a simple image creation device. Go in with a relatively well conceived perspective and begin shooting your real world location without focusing on creating accurate representation. Try lowering your shutter speed well below 1/60 to invite in motion blur and purposely take your aperture out of fine focus. If you have light control you may want to begin working on backlighting or very sharp lighting formats, hyper realizing the key light and losing the fill light altogether. This will create silhouettes, sharp contrast, and a very dramatic sensibility.
If you are working in a photo editing program, you have even more that you can do as making dramatic changes to your photos will only take a few moves. A good example of this can be to desaturate the image, raise the contrast, and blow out certain areas. What this will do is resemble crime photography, which takes the original photo out of its context and then allows the viewer to correlate it with the cultural institution of the crime photographer. This will initiate the image as surreal photography because the juxtaposition will be in place, though it will be between the image and the style.