--One approach is to replace the portion of the pig's DNA so that the pig's organs appear to be
compatible with a specific human.

--A second approach is to transplant the organ from the pig when the pig is still in its embryonic state.
http://news.nationalgeographic.com/news/2005/02/0215_050215_transplant.html

"By implantation of pig embryonic tissues into immune-deficient mice, we have now determined for
the first time distinct gestational time windows for the growth of transplanted pig embryonic liver,
pancreas, and lung precursor tissue into functioning tissue," said Yair Reisner, a professor in the
department of immunology at the Weizmann Institute of Science in Rehovot, Israel.

Using pig tissue to replace failing human organs could help patients with diseases such as diabetes,
Parkinson's, and liver failure.

--A third approach is to eliminate the genes in the pigs which cause the human's immune system to
reject the organ.  This approach is being tried in England by the scientists who created Dolly the
cloned sheep.
http://www.rideforlife.com/archives/000177.html

Xenotransplantation is the transplantation of an organ from one species to another.