It depends on where the abscess is found. In essence, an abscess is a collection of pus which usually is a thick liquid made up of necrotic tissue, white blood cells and often bacteria. If this collection is on the body surface, it can be drained with an incision and the contents extracted.
Often, this can be done using topical anaesthesia. Otherwise, general anaesthesia may be used, especially if the abscess is large or when it is in a sensitive location. If the abscess is in a deep location, it may have to be drained with radiological guidance and by inserting a drainage tube into the abscess cavity.