Kohler and Milstein (1975) were the first to demonstrate that somatic cells could be fused with murine myelomas and that monoclonal antibodies with unique specificities could be produced. A vast array of monoclonal antibodies have now been produced. In the generation of most monoclonal antibodies, mice are immunized against a specific antigen, and their cells are fused with the mouse myeloma cell. The procedure is as follows: (1) spleen cells from immunized mice are fused, using polyehtylene glycol, with myeloma cells which are rendered drug sensitive by a mutation in a growth essential gene HGPRT (hypoxanthin-guanine-phosphoribosyltransferase). (2) the cell mixture is then cultured in medium containing the selective drug. The immune cells, although not sensitive to HGPRT, survive for only about one week in culture. The myeloma cells are drug senstivie and die within a week. The only cells that survive are those hybrid myeloma cells that obtained a normal HGPRT gene from the immune cells. These hybridomas can grow continuosly in vitro and some secrete antibody. (3) Using appropriate screening technology, clones of cells that secrete antibody of interest can be identified and expanded in vitro or in vivo to obtain large quantities of monoclonal antibody that can subsequently be purified to homogeneity.For more information see (Nelson, J Clin Pathol: Mol Pathol 2000, 53: 111-117) and for an 

example protocol of this method see (US Patent Application No 12/596747; Okumura (US2006/246550).  See also Greenfield “Geernating Moncolonal Antibodies, Chapter 7, 2014 Cold Spring Harbor Laboratory Press)

A more detailed procedure is the following: 1st, B-cell hybridomas are formed by fusing primed B cells and myeloma cells. This procedure involves 1) priming a mouse with a given antigen. 2) fusing spleen cells from that primed mouse with mouse myeloma cells using plyethylene glycol. The myeloma cells have the immortal growth properties of a cancer cells but do not secret their own antibody gene product. The myeloma cells also lack the ability to produce an enzyme known as HGPRT which is necessary in the synthesis of nucleotides by the salvage pathway. 3) Growth of the cells on a HAT medium which contains aminopterin which blocks the synthesis of nucleotides by the de novo pathway. When the de novo pathway is blocked, cells try to synthesize nucleotides by the salvage pathway. Fused hybridomas will be able to do this since they will contain the full complement of necessary enzymes (spleen cells which are HGPRT+ ) but myeloma cells which have not fused will not be able to grow. Unfused spleen cells do not need to be selected at all because they are terminal cells.

2nd, the resulting clones are screened for those clones which secrete the antibody with the desired specificity. The supernatant of each hybridoma culture contains its secreted antibody and can be assayed for a particular antigen specificity as by ELISA (antigen that reacts with the desired antibody is bound to microtiter wells).Once the hybridoma secreting a monoclonal antiboyd of the desired specificity has been identified, it is growth in tissue culture flasks or can be grown in the periotneal cavity of histocompatible mice.