The overall process is as follows:
A primer that matches the beginning of the DNA to sequence is used to synthesize a short DNA strand adjacent to the unknown sequence, starting with the primer (see PCR).
The new short DNA strand is sequenced using the chain termination method.
The end of the sequenced strand is used as a primer for the next part of the long DNA sequence, hence the term "walking".
The method can be used to sequence entire chromosomes (hence "chromosome walking"). Primer walking was also the basis for the development of shotgun sequencing, which uses random primers instead of specifically chosen ones.