DISCLAIMER
I do not have a medical license, and I am not distributing medical advice. Ask your primary care physician for more information.
Overview
The Immune System is made up of two main parts: the adaptive immune system, and the innate immume system. The innate immune system attacks all pathogens upon sight. The adaptive immune system takes more time to boot up, and is more effective.
The Innate Immune System
Let's meet the players of the Innate Immune System.
Macrophages
Macrophages are large soldier cells that sit stationary in tissue, or course through the blood and lymph. They ingest pathogens by extending their cytoplasm (skin) to engulf the pathogen. The pathogen is then broken down as enzymes are mixed with the pathogen. Macrophages in the lungs are called Alveolar Macrophages, and they are careful to not damage lung tissue. Macrophages can sense pathogens through chemotaxis (Wikipedia link).
Neutrophils
Neutrophils are the crazy fighters of your body. They release toxic chemicals that kill many bacteria, but also damage healthy cells. During a viral infection, Neutrophils do more harm than good. Neutrophils can form a Neutrophil Extracellular Trap (NET) by coating its DNA with lethal proteins, and expelling it in a ring around the cell. For those reasons, Neutrophils kill themselves frequently to avoid too much collateral damage.
Monocytes
Monocytes are cells in your blood that can become Macrophages if there is an infection.
Inflammation Cells
There are 3 main types of inflammation-causing cells, and they are responsible for allergies and asthma.
Mast Cells
Mast Cells prime themselves with antibodies, and when they detect a trigger, they flood the blood and tissue with histamines, which cause massive inflammation.
Basophil
Basophils continue the inflammation caused by the mast cells.
Eosinophils
You only have a few Eosinophils, and they make sure you feel horrible for a few days after the allergen is first exposed to you.
Complement System
The complement system is a system of proteins that swarm around the blood at all time, in the millions. They make bacteria easier for Macrophages to ingest, maim enemies, and poke holes in things until they die. It is incredibly complicated.
Natural Killer Cells
Natural Killer Cells are cells that check if cells are producing MHC Class I molecules. MHC Class I is a "window" into a cell to see what it is doing. Most cancerous cells and virus-infected cells stop producing MHC Class I to hide their shady insides. Natural Killer Cells kill those cells.
Dendritic Cells
You may have been wondering if there is an MHC Class II Molecule. There is! Dendritic Cells take dead bacteria/virus bodies and show them to your Adaptive Immune System in MHC Class II Molecules. The Adaptive Immune System is picky that way.
The Adaptive Immune System
Here are the main cells of the Adaptive Immune System.
T Cells
T Cells are born in an organ known as the thymus, which is an organ between you lungs. T Cells have receptors on them, which check for certain chemicals. In the thymus, T Cells are tested on their receptors. When a T Cell's receptor is activated, it causes a immune response. The thymus tests whether the receptors work, the receptors don't respond to your own body (if they did, you would fight yourself), and if the T Cells can communicate effectively. If a T Cell does not pass all these criteria, it is killed.
Helper T Cells
The first main type of T Cell is a Helper T Cell. When the Dendritic Cells make their samples, they bring the samples to your T Cells. When a Dendritic Cell find the right T Cell, the T Cell clones itself to make a small army of Helper T Cells. Helper T Cells encourage your Macrophages to fight harder, and keep them from killing themselves. They also activate B Cells. After an infection, some T Cells wait for the same infection to happen again, and activate your defenses quicker and better.
Killer T Cells
The other type of T Cell is your Killer T Cells. They are activated by Dentritic Cells, but only partway. Helper T Cells fully activate Killer T Cells. Killer T Cells kill your own cells if they are infected by viruses. After an infection, Killer T Cells hang around and wait for another infection of the same type, and then start killing.
B Cells
B Cells are produced in your bone marrow, and also have specific receptors. The B Cells are trained in a similar way to T Cells, but in the bone marrow. When B Cells get activated, they produce their receptor in the thousands, and vomit them out. These are called Antibodies. B Cells are activated by parts of pathogens in lymph, but only partway. Helper T Cells fully activate the B Cells into Plasma Cells. Plasma Cells are super B Cells and pump out a huge amount of Antibodies. After an infection is over, B Cells become Memory B Cells and wait for the same pathogen, then start pumping out Antibodies. Plasma cells become Long-Lived Plasma Cells and pump out Antibodies all the time.
Antibodies
Okay, so what the heck are Antibodies? Antibodies are little tiny proteins that attach to bacteria and viruses and cramp to them, and even latch viruses to each other. Imagine if a bunch of crabs were pinching all around you. Those are antibodies.