This paper describes the most important (IMHO) technical breakthrough in the biological sciences: DNA sequencing using a single-stranded DNA template, a DNA primer, a DNA polymerase, radioactively or fluorescently labeled nucleotides, and modified nucleotides that terminate DNA strand elongation.
Prior methods depended on partial hydrolysis and were painfully slow. It was a big deal when Gilbert and Maxam reported in 1973 the sequence of a whopping 24 basepairs using a method known as wandering-spot analysis. Contrast this to the ~3 billion base pair human genome. Clearly the process needed to be sped up in order to be useful.
The key innovation of the Sanger method was the use of dideoxynucleotides triphosphates (ddNTPs) as DNA chain terminators. The basic idea is that the florescently labeled ddNTPs will stop chain replication wherever they are incorporated into an elongating DNA strand. DNA fragments of various lengths are separated by electrophoresis and the fluorescent tags are "read" give the nucleotide sequence. The whole procedure relatively simple and is adequately described in wikipedia.
Figure: a typical sequencing four-color chromatogram.
Sanger et al.'s technique was used to determine the sequence of the DNA bacteriophage PhiX174 which contains 5,386 nucleotides, the first DNA based organism ever to have its complete genome sequenced. (The first organism was MS2, an RNA bacteriophage).
It is true that the process was eventually sped up using thermally stable (e.g. Taq) DNA polymerases, capillary electrophoresis and dedicated thermal cyclers, but the basic technique is still used today.
Alas today, chain termination sequencing is being replaced by newer quicker methods, especially pyrosequencing. Chain termination methods are probably inadequate to compete for the Genomics X prize given to the first team build a device capable of sequencing 100 human genomes within 10 days or less with an accuracy of no more than 1 error in 100,000 base pairs, with sequences accurately covering at least 98% of the genome, and at a demonstrated cost of no more than $10,000 per genome.
Frederick Sanger was awarded his second Nobel Prize for this work in 1980.