The "basic's of cleansing are pretty simple. I use this to cleanse my home of any negativity that may be around. First I make a smudge stick. I, personally, use herbs that I have grown myself if possible. White sage is a common ingredient in these, as well as rosemary, lavender, pine, cedar, and many more. Use what you feel will work for you or your home.
Take these items and bind them together with yarn, thread, anything that will burn. You can also wrap these in a paper with sigils, or a written chant for cleansing. Make sure you have something to extinguish the fire, or to carry this in if you need to. Don't burn anything without using common sense, obviously.
As you burn this and it begins to smoke, visualize any negativity being wrapped in smoke and carried from your home, to be put back in the universe for reuse. I usually also have a chant ready to say while cleansingmy home or property. When you are finished, you can do a protection spell, make wards, sigils or whatever you choose to protect your home.