Good news! Detoxification is a totally normal process and it is happening in your body all day, every day. The main organs of detoxification include the liver, the kidneys, the skin and the lungs. Proper detoxification requires a good digestion providing a full range of required nutrients to run smoothly, and it requires good circulation.
It is possible to have symptoms from poor detoxification, and many conditions are aggravated by a lessened ability to modify and excrete the many types of compounds that must be removed from the body.
I would however, caution against a one size fits all approach! Knowing what you are trying to detoxify will help to determine what the approach is.
Some common approaches to detoxification do not really detoxify anything on a molecular level. For example, some of the most popular detoxes on the market are merely laxatives. Although that approach will no-doubt, improve the amount of stool excreted, it will generally only make you feel better if you are constipated. It does not however, improve the chemistry of detoxification. For more details, listen to the short detox podcast, or take a look through the Start Here, Start Now course for the detoxification lecture.