Specific Immune Responses..Watch
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.