How does a tooth extraction actually work?

Not sure your ??: If you need an extraction...You'll go to a dentist or oral surgeon (specialist) and they will x ray your tooth(teeth) and determine what needs to be removed. They will numb you up accordingly, and remove the offending teeth. It could be a simple extraction or they might need to remove bone or tissue. They'll know and they will let you know ahead of time.

From easy to complex: Once complete anesthesia is confirmed (only pressure no sharp feeling) tooth extraction can range from very easy with just moving loose teeth with an elevator instrument to complex if teeth are impacted underneath gum and bone tissue. In these instances, tissue is carefully retracted, bone surrounding the tooth removed and at times the tooth sectioned in portions so that the pieces can be removed.

Work?: You mean how is an extraction done, or why extract a tooth? Extracting a tooth removes the source of a problem (pain, swelling, infection, decay), makes more room for the other teeth, and/or improves the prognosis for the remaining teeth. A tooth is extracted by separating the root from the bone. If the tooth is impacted or stuck, sometimes sectioning the tooth is necessary.