The human genome was sequenced by two different groups in two different ways. The $3 billion US Dollar (USD) Human Genome Project (HGP), supported by the US Department of Energy, used a technique called "hierarchical shotgun sequencing", where it broke down the human genome into pieces consisting of 150,000 base pairs each. These pieces were then put inside bacteria where the bacteria's DNA replication machinery makes many copies of the sample for easier sequencing. These constructs are called bacterial artificial chromosomes. The project was founded in 1990 and took 13 years to complete, reaching its end in April 2003. A "rough draft" of the human genome became available in April 2000.
Another group, Celera Genomics, used a relatively novel approach called whole genome shotgun sequencing to sequence the human genome in much less time and at far lower cost ($300 million USD) than the federally-funded HGP. This group started in 1998 and finished in 2001. Whole shotgun sequencing involves breaking up multiple copies of the genome into smaller parts randomly, sequencing those parts, and then determining which parts connect up with which by seeing where the codons overlap. Supercomputing and sequencing algorithms contributed invaluably to the Celera approach, making it feasible. Prior to Celera's work, the largest genome sequenced through the whole shotgun approach was about 13 million base pairs, far short of the human genome's three billion base pairs. It is important to note that the Celera project did not start from scratch as the HGP did though; it was able to access existing information that had been previously published on GenBank, a collection of genetic sequences and data available to all.
Despite the human genome containing three billion base pairs, only 3 percent codes for proteins (the other 97 percent being junk DNA), creating a total of about 25,000 genes. This is small compared to estimates of 40,000 to 2,000,000 genes being tossed around prior to the completion of the project. The finiteness of the human genetic code means that it is feasible that one day, researchers be able to understand human genes in their entirety and even manipulate them.
Work continues on analyzing the work that came out of the HGP. The latest initiative is to find a way to sequence a human genome for less than $1,000 USD, which would make the technology feasible for wider use. A single sequencing could determine many important genetic characteristics of the person, including your likelihood of developing certain diseases. Craig Venter, former leader of the Celera project, has had his genome entirely sequenced and has spoken with various media outlets about the results and their implications.