I own the identical Rolex Submariner. It's the most faked watch in the world, but comparing this one to mine it certainly looks genuine.
The cyclops eye magnifier over the date is a good indicator that it's real. The fakes don't actually magnify the date.
Also, the wording on the face appears identical to mine; on the fakes it's typically larger and in other ways different.
Of course, if it's working, that the best sign as fakes wouldn't withstand being lost at sea.
Quick tip to tell a real Submariner: the bezel only moves in one direction; with fakes the bezel will move in both directions.
Another tip for Rolex: Rolexes have sweep second hands, this means they move smoothly instead of in a jerk for each second. It used to be that a sweep second hand was a good sign you had a real Rolex, but it means nothing now as many fakes have Japanese movements with sweep second hands. If you listen to one of these fakes, you'll hear that the movement crashes and bangs like a middle school band, whereas a real Rolex movement is quiet and smooth.