Cells can increase and decrease their sensitivity to cells by regulating the number of their receptors. Remember that receptors are proteins and are manufactured by the cell itself, so a cell can increase and decrease the amount of receptors within its plasma membrane. If a cell increases the number of receptors then we call it up regulation; and if the cell decreases the number of receptors we call it down regulation.
Up regulation is used by cells to increase their sensitivity to a specific hormone. Up regulation occurs when a cell produces more receptors, the cell decreases its degradation of receptors or by activating already present recpetors. Cells typically up regulate when the concentration of a hormone is very little. If there is a lower concentration of a hormone in the blood stream and the cell increases the number of receptors, it increases the chances of interacting with that hormone (sensitivity). Hormones themselves can also cause cells to up regulate.
Down regulation is when a cell decreases its sensitivity to a hormone by decreasing the amount of available receptors. To understand this just reverse everything mentioned in the up regulation paragraph.
Hormone clearance is the process of lowering hormone levels in the blood through two mechanisms: decreased secretion of a hormone and/or increased degradation of a hormone. Hormones can be broken down by their target cells by the enzymes that remove them from receptors, are degradated in the blood (another factor with the shorter half life), or circulate to the liver and are broken down. All three of these steps leads to excretion from the body via bile (steroid hormones) or via urine by the kidneys.
Here is a link so you can see this in action: http://www.physiol.med.uu.nl/interactivephysiology/ipweb/systems/buildframes.html?endocrine/biosec/01
Source: Mind of Aaron
Source: Self made