If you're talking about monoclonals then there are several different types as Wangers says.
1. Animal monoclonal antibodies
Usually of mouse origin. Mice are immunised with the antigen of choice and then high affinity antibodies are produced by isolating B-lymphocytes and immortalising them.
However using these antibodies in humans presents problems, as they are from mouse they illicit an immune response in humans. Which can be potentially fatal.
2. Chimeric Antibodies
As the fact the antibodies are of mouse origin is what's causing the problem, chimeric antibodies hope to reduce this by cutting and pasting the variable regions of the mouse antibody (which contain its binding activity) onto human constant regions. This is where some recombinant DNA tech is used, presumably fusion PCR.
3. Humanised Antibodies
Chimeric antibodies still have a large area that is of mouse origin. However, looking at the variable regions only certain residies within regions called complimentarity determining regions (CDRs) actually contain the binding activity. Therefore, using human antibodies as a frame work, these residues replace the ones in the human antibody.
I guess the DNA tech used here is more Site Directed Mutagenesis or casette mutagenesis.
4. Human antibodies
Despite the drastic reduction in mouse residues, humanised antibodies still have some. The solution is to make fully human antibodies, with no mouse residues involved at all. Now this, for ethical reasons, can't be done by immunising humans with the antigen. Instead huge DNA libraries of millions of potetinal antibodies have been created. These then need to be screened against the antigen to see which ones bind the target. This is done via display technologies such as Ribosome Display, Bacterial Display and Phage Display that couple phenotype (the antibody and its ability to bind/not bind) with its genotype (the DNA sequence encoding that antibody)