Let's start by making a distinction between cleaning and clearing your crystals.
Cleaning involves wiping the dust off of them pretty much the same way you'd clean anything in your home. This can be done with a soft damp cloth. The exception to that is when you're cleaning soft or soluble stone such as selenite, halite (your salt lamps for instance), opals, turquoise, to name a few, or stones that can be etched by the acids in your water, depending on your waters pH levels, such as fluorite, pyrite, gypsum. If you have a high iron content in your water it can also stain certain stones. I have never had an issue with staining but I also don't have a high Fe level in my tap water.
Clearing or cleansing your stones involves what I think of as resetting them. The purpose of this is to return it to its natural state. I don't believe that stones get energetically "dirty" but they can get a bit clogged if exposed to strong negative energies or trauma, and left too long without a clearing. Years ago I had a smoky quartz pendant, that I was wearing for protection, crack on the inside. It was pretty disturbing but made sense considering the stress I was going through during that time. In that case I immediately stopped wearing the stone and tossed it in the ocean. The philosophy behind this is that the stone did what it was supposed to, absorbing the negative energy, and unfortunately may have absorbed more than its structure allowed, the consequence of which was a crack or break. It's best then to return it whence it came-Mother Nature.
You've probably also heard talk of needing to charge your crystals, or that some crystals never need to be cleared or cleansed.
I believe all crystals need a reset now and then.
If you feel like your crystal needs a charge put it in the moon light on a full moon. Alternately you could put it in the morning sun light but some stone will fade in direct sun light. This list includes amethyst, citrine, smoky quartz, aquamarine, celestine, danburite, kunzite, hiddenite, and fluorites. This is not a complete list so check on the properties of your stone before you subject it to a tanning session. Try to do this at least once a month, or any time you feel a fogginess or dullness coming from your stones.
My favorite ways to clear and reset my stones are by smudging them or exposing them to sound vibrations.
To smudge I use a Palo Santo stick, lighting it and then blowing out the flame so that it produces a nice thick smoke that is wafted around the stone. You'll notice that the smoke seems attracted to the crystals. Sage bundles are also widely used.
With sound I place the stones that are small enough, in a singing bowl and rim the bowl until I get a nice steady tone. Let your intuition tell you when it's enough. If your stones are too big for a bowl, you can play the bowl, or gong, or any other instruments that will give a nice vibration, near the stone. You can even achieve the same effect by placing the stones near a speaker with the volume high enough to emit a noticeable vibration.
Keeping your stones charged and cleared will make for happy stones.