Digital camera sensors suffer from an inherent amount of noise that bleeds into their images during very long exposures. This noise is a result of heat in the electronics within the camera.
As the camera makes the long exposure, it is slowly gathering light through the lens, which constitutes the "signal" part of the image being created. Meanwhile, as long as the shutter is open and the sensor is active, the noise from the in-camera electronics is added to the "signal" (just the image data) which gives the overall end result of the photograph being "signal + noise."
If we want to remove just the noise, immediately after we are done with our long exposure, we can create an additional photograph with the lens cap on the camera lens which will provide a frame that is no signal, and 100% noise.
Then, by use of specialized techniques in Photoshop, we can subtract the "noise" from the "signal + noise" which will then give us just the clean "signal" or image without the long exposure noise. Voila: clean images!
If you have "Long Exposure Noise Reduction" (or "High ISO Noise Reduction") on in your camera, then this is exactly what it is doing, all by itself. Chances are you probably noticed your camera taking TWO images for every long (or high ISO) ONE you tell it to take. What is it doing? Dark Frame subtraction! In some cases, this is great and you wouldn't want to go through the trouble of doing it yourself in the way I am about to lay out.
Personally, I like to retain control over 100% of the noise reduction in my workflow, so I have these options turned OFF in my cameras. I am frequently asked during classes which is the best approach - and the answer is the one I always hate to give - "it depends." Each camera is different, and my advice is to experiment in your backyard with long exposures in ALL possible combinations of Long Exposure / High ISO noise reduction settings (including OFF and doing the dark frame yourself) - and then carefully examine your images on a computer to see which is better.
So you want to do your own Dark Frames! Great. The first and most important step is remembering to shoot them IMMEDIATELY AFTER you shoot your long exposures. Noise as I said above is a factor of temperature, so if you forget to shoot your Dark Frame right after your Long Exposure and think you can do it later before you got o bed after your camera has been in your bag/car etc., the temperature of your sensor will be slightly different, and the subtraction technique won't work. Here's a Step By Step:
Step 1: Make sure "Long Exposure Noise Reduction" is OFF if you plan to take dark frames.
Step 2: Shoot your long exposure photo as normal.
Step 3: As soon as your image is safely written to your card, place the lens cap on your camera and take an IDENTICAL image (same length, same ISO). Take extra care that your eyepiece viewfinder is covered, and that no headlamps or external light sources are shining at the lens of your camera. Even a few errant photons can negate this entire exercise.
Step 4: Pull out your phone and record the file #s of the image and the dark frame, and make note of which is which. You'll obviously be able to tell later in Lightroom, but it's handy if you take many to know.
Step 5: Post-Processing. Make sure to synchronize ANY AND ALL develop settings made to the Photo RAW file with your dark frame.
Step 6: Open both files as layers in Photoshop with "Edit In / Open As Layers In Photoshop" command.
Step 7: In Photoshop's Layers panel, place the dark frame ABOVE the image.
Step 8: Change the blending mode of the dark frame to "SUBTRACT." At 100% zoom, it should be obvious now when toggling the "eyeball" of the Dark Frame layer on/off that the noise is being removed from your image.
Step 9: SAVE!
That's it. Here is a >100% crop of the above image, on which I have used this technique. As you will see, it's not 100% perfect, but it does knock back a lot of the noise.