Site directed mutagenesis an efficient strategy for implementing mutations in a plasmid. In the simplest case the strategy can modify or insert a few nucleotides. In more complicated cases a sequence of arbitrary size can be incorporated into any plasmid.
The basic idea is that since a PCR primer is incorporated into the dsDNA final product of a PCR, any nucleotide modifications in the PCR primers will be incorporated into the final sample of dsDNA. Further, by including significant homology in the 5' ends of the primers, the primers will prime each other to facilitate ligation of the ends of a strand of dsDNA. If only two primers are used on a plasmid then the primers will circularize the product to create a plasmid containing the mutation of interest.
The biggest concern in the design of site directed mutagenesis primers is that for the reaction to occur efficiently, the primers need to preferentially bind to the template rather than themselves in spite of their 5' homology. This can be addressed by purposely designing the primers such that the 5' region anneals only to the other primer while the 3' end anneals only to the template.
To design primers for simple site directed mutagenesis, one needs to consider three annealing events and as a result, one needs to design for three Tms. The 3' end of each primer need to anneal to the template strand for amplification. Then the 5' end needs to anneal to each other. This Tm can be designed as a hybrid sequence whereby the nucleotide sequence on the 5' end of both primers can be considered as one nucleotide sequence. The 3rd Tm is for this overlap sequence.
The mutagenesis PCR reaction itself is a standard PCR with high fidelity polymerase to reduce incorporation of point mutation due to the fidelity of the polymerase. At the end of the PCR, one would expect a running at the length of fully linearized DNA. DPNI digest post mutagenesis is usually standard.
In my work I typically use Phusion(r) NEB in HF buffer with 5% DMSO but any PCR strategy using a HF DNA polymerase should be sufficient.
From David Shis's Thesis