When a tooth is badly damaged or decayed and can't be repaired (or will be very difficult to repair), you may opt for an extraction. The extraction will normally be completed under a local anaesthetic. You will feel pressure as the dentist loosens the socket of the tooth, but no pain.
More complicated extractions (or several at the same time) may be completed under general anaesthetic, at a hospital. These treatments are performed by an oral surgeon who specialises in this type of treatment.
It is important that you tell your dentist about medication that you are taking. There are normally no adverse reactions from an extraction and within a few hours or the next day, you will be feeling ready for work etc.
Your dentist will discuss further treatment options to deal with any gap that is left.