How do white blood cells fight pathogens?
Through 2 mechanisms, innate and acquired immunity.
The innate immune response, WBCs as macrophages, dendritic cells, monocytes. They cause inflammation, swelling, tenderness as part of immune response due to secretion of neurotransmitters that activate other WBCs (cytokines and interleukins), and to cause dilatation of blood vessels to allow for more WBCs to come (histamine). This type is generalized for all pathogens.
The acquired immune response takes more time than innate - as it is specific for each pathogen. Major players are B and T cells. B cell that binds to the pathogen (antigen), is activated - then by the help of Helper T cells, procreates generating plasma antibodies to fight the pathogen, and memory cells to remember the pathogen if entered the body again. For the acquired immunity to work, we need antigen-presenting cells as macrophages and dendritic cells.
In case of intracellular pathogens, infected cells generate abnormal antigens, easily identified by Cytotoxic T cells, which then binds to these cells causing them to die.