Kyanite and Citrine are the only 2 crystals that never need cleansing. For everything else there are various methods that you can use.

Water
As simple as washing it down. However be careful that some don’t work well with this method like Lapis Lazuli or Selenite. This works best for tumblestones. Don’t use this for clusters as well that may break apart with contact with water for longer periods.

Fragrance or Smudging
You can use Sage, Frankincense, Palo Santo, Incense sticks of Pine, Juniper, Rose, Lavender, lemongrass or cedar smudge stick. Circle them in anti clockwise spirals 3 times over the crystals and let them burn near the crystals. This is my personal favourite method as you cant go wrong with it incase you are unsure of what method is not suitable for a specific crystal type.

This will also cleanse the room where you burn it so it serves a dual purpose.

Mother Earth.
Bury them in soil for 24 hours and once done just brush of the dirt and its ready for use. If the stone is delicate just place it in an open ceramic dish on top of the soil to achieve the same results.

Sound
Collect a bunch of crystals to be used and use the sound of a hand bell, tibetan bells or singing bowls over them.

Sunlight
Some stones work well with sunlight such as Topas or Diamond. Leave them in the sun from morning until noon. You can also substitute a candle with gem stones placed around the candle in a circle until it goes out naturally or burns through. Some stones do not work well with sunlight such as Aventurine, Amethyst, Aquamarine, Citrine, Smoky Quartz, Sapphires, Flourite, Beryl and Rose Quartz.

Moonlight
A night of a full moon is also very effective in cleansing crystals such as Rose Quartz, Moonstone, Selenite and Amethyst. This goes for other crystals as well that as translucent or transparent or have clouds or inclusions in them.

Salt
Be careful while cleansing with this method as it can scratch the crystal surface. alternatively you can form 3 clockwise circles of salt around our crystals and leave them in it for 12 hours. When done, dissolve the salt in water and wash it away with running water. You can even leave the crystals in a ceramic dish on top of a large bowl of salt for 12 hours.

Infusions
Infusions can be made with a tsp of rosemary or hyssop or sage in a cup of boiling water. stir this, cover and leave it for 10 minutes; strain, let cool and this is ready to be used. Amethyst can be soaked in cold water for a few hours and the water can be used as an infusion. Spray this on the crystal and wipe clean with a soft cloth. For delicate stones, you can place dry herbs such as thyme, sage, rosemary and hyssop in a big bowl and lay your crystals in a smaller ceramic dish within this mix for 12 hours.