The drugs used as anti-pyretics are paracetamol (acetaminophen), asprin and other non-steroidal anti-inflammatory drugs (NSAIDs), and corticosteroids. It is rare to use the corticosteroids for this purpose though, since the others are as good or better and have a far less broad effect on the body.
To understand why antipyretics work, you need to know a little about how fever (pyrexia) comes about. Techically, any source of inflammation can cause a fever, although the most common and powerful cause is an infection. Inflammation is regulated by small proteins called 'cytokines' which are produced by the immune cells to signal to each other.
So, an inflammatory state is abuzz with buckets full of cytokines in the blood. When the blood reaches the brain, some of the cytokines in it (for what it's worth, especially IL-1, IL-6 and TNF) trigger the release of a substance called prostaglandin E2 from the endothelium near the hypothalamus. This sets off a chain reaction in the brain that raises the body's set point temperature, thus causing fever. Also, microbial toxins (e.g. bacterial cell wall fragments) can do the same as the cytokines by binding to different receptors on the hypothalamic endothelium.
Now for the anti-pyretic medication. Prostaglandin is formed from a cell wall phospholipid, called arachidonic acid. It is 'broken off' the cell wall by an enzyme called phospholipase A2. Corticosteroids inhibit this step.
Thereafter, arachidonic acid be used to form either of two groups of substances. The process of turning it into a prostaglandin is catalysed by the enzyme cyclooxygenase. This enzyme is inhibited by aspirin and the NSAIDs, and by paracetamol (acetaminophen).
Thus, in both cases, prostaglandin E2 production is reduced, lowering the fever.Hope that helps. It is a bit complicated, but at least it's a logical process.
There's a reasonable picture of the pathway I described here: http://www.arthritis.co.za/images/nsb.gif