Specific Immune Responses..Watch this thread
Lymphocytes basically bind to the antigens of pathogens. Think of it as uniquely shaped protrusions on the cell membrane of bacteria, and different pathogens have differently-shaped antigens. So the lymphocytes then produce things called antibodies, which basically stick to the surface of the pathogen, and act as a flag for the phagocytes to identify the pathogen.
Phagocytes search out the pathogens, and then engulf them, before digesting it with enzymes. Pretty simple.
Another point - memory lymphocytes also retain their memories of the pathogen so they can identify it when it invades the body again - it's why your body becomes resistant to diseases you have caught before. They also produce antitoxins to negate any toxins the pathogen might produce.
That's about it, hope it helps.