Very over-simplified: You have a random library of many billions of cells each making a single unique antibody that was created via random combinatorial genetic shuffling early on. The ones that accidentally bind to your own natural proteins are filtered out by killing them before they leave the bone marrow, so the circulating cells remaining form a library that could only bind -foreign- proteins. When one of these foreign-binding-cells in the library actually binds a foreign protein this cell multiplies like crazy and eventually the clones secrete free floating versions of the antibodies that neutralize the protein it detected, some of these clones stick around in the bone marrow to form a long-term memory-library of previously activated antibodies.

There are actually two separate systems: the T cells and B cells. I recommend the very readable Lauren Sompayrac's "How the Immune System Works". Or google/wiki "clonal selection" and "VDJ recombination".