Small items can be cleaned by immersing them into water that has been dedicated and blessed for this purpose. (Provided they can go into water.) They can also be wiped down with appropriately blessed water. When I am wiping an item down with blessed water, I like to keep a small container of plain water. My method is to dip my clean cloth into the blessed water and then wipe a section of the item. Then, I rinse the cloth in the plain water before dipping it into the blessed water. Much like cleaning with old fashioned soapy water, the plain water holds the spiritual 'dirt' and dramatically cuts down on how much of it muddies the blessed water.
When the item can not go into water or have water applied to it, it is possible to place it within a container of salt for a period of time. The salt will draw out the spiritual pollution. When I can, I place the item upon a bed of salt and then cover it with another layer of salt, thereby allowing the spiritual pollution to be removed from all surfaces of the item at the same time. From what I have been able to tell, this works faster then just having the item partially covered in salt.
I also have buried items in the ground for a period of time to 'earth' the spiritual energies associated with the item. This serves to 'reset' the item to a spiritually neutral state, provided that the miasmic build up is not to a very severe extent. In the event of an item having a high concentration of miasma, I use this as my final step in cleansing the item, when it is appropriate. The time to bury an item in the earth or in salt is one that is subject to some debate.
Some practitioners of magic have found that the length of time should be one lunar cycle. Others have found success in three days. It is good for the person who is doing the cleansing to pick a time frame that is meaningful to them. The cleansing action is partly done by the materials used and partly done by the practitioner's intention.
Moving the item to be cleansed through it or wafting the smoke towards the item can be used to 'smudge' said object. I have found that smudging is a helpful practice when used in conjunction with other spiritual cleansing practices. Others have found that smudging is effective on its own. In this, like determining the time frame that the object must be buried, one must listen to their inner senses and monitor the progression of the object's cleansing.
For larger items, it is impractical to bury them in salt or soil. It is often the case that one has a larger item, such as an heirloom dresser, that has spiritual grime attached to it. This item can be cleansed by asperging it with blessed water and driving out the spiritual essences of the 'grime' with prayers. It is also possible to use incense in the smudging fashion with prayers. The prayers (or incantations, if you wish to call them that, either is accurate in my opinion) are a projection of the practitioner's intent to remove the miasma. With sufficient focus and strong enough intent, it is possible to remove a significant amount of spiritual pollution by way of just prayer alone.
Many magic practitioners like to cleanse their ritual tools prior to first use. This is a helpful thing that allows one to set their ritual tool to a 'default' neutral magical state. As one uses their ritual tools, they acquire residual spiritual energy. Regular cleansing of ritual tools helps to make them more effective. Initial and maintenance cleansing have subtle differences. Initial cleansing, the practitioner focuses upon removing all acquired spiritual resonance signatures. It is a very through cleansing. Maintenance cleansing removes the spiritual resonances that are not desired. This allows one to tailor the spiritual energy signature of an item to the purposes they desire to use the item for.
Incidents of mild to moderate spiritual pollution upon one's ritual tools generally merits a maintenance cleansing. One method used is frequently sufficient to cleanse the item of undesired spiritual energy. In cases of severe to extreme spiritual pollution, multiple methods of cleansing bring about greater success. For an item that is heavily tainted with miasma, it may be necessary to spiritually cleanse it multiple times before it is restored to that 'neutral' state.
It may also happen that an item is so heavily tainted with spiritual pollution that one person's efforts simply are not enough to resolve the problem. This is where one invokes the assistance of deities and their spiritual community. Prayer, when married to practical action, can be powerful enough to lift or at least ameliorate severe spiritual pollution. One must recognize, however, that there may be cases where the spiritual pollution is simply so severe that it will linger for an extended period of time, despite one's best efforts.
If one must handle or work with an object that is so spiritually tainted that cleansing efforts only has a minimal effect, it must be treated with care. Personal cleansing after handling or interacting with said item is a must. Cleansing items that come into contact with the tainted item is also very important. This helps to control how much the spiritual pollution will spread.