There are a number of tools available in the Tools page of the 1000 Genomes Browser.
Our data is in standard formats like SAM and VCF, which have tools associated with them. To manipulate SAM/BAM files look at SAMtools for a C based toolkit and links to APIs in other languages. To interact with VCF files look at VCFtools which is a set of Perl and C++ code.
We also provide a public MySQL instance with copies of the databases behind the 1000 Genomes Ensembl browsers. These databases are described on our public instance page.