To call variants with the GATK using pedigree information, you should base your workflow on the Best Practices recommendations -- the principles detailed there all apply to pedigree analysis.
But there is one crucial addition: you should make sure to pass a pedigree file (PED file) to all GATK walkers that you use in your workflow. Some will deliver better results if they see the pedigree data.
At the moment there are two of the standard annotations affected by pedigree:
Note that you will need at least 10 founders to compute the inbreeding coefficient.
In the specific case of trios, an additional GATK walker, PhaseByTransmission, should be used to obtain trio-aware genotypes as well as phase by descent.
The annotations mentioned above have been adapted for PED files starting with GATK v.1.6. If you already have VCF files generated by an older version of the GATK or have not passed a PED file while running the UnifiedGenotyper or VariantAnnotator, you should do the following:
-G StandardAnnotationto VariantAnnotator. Make sure you pass your PED file to the VariantAnnotator as well!
The PED files used as input for these tools are based on PLINK pedigree files. The general description can be found here.
For these tools, the PED files must contain only the first 6 columns from the PLINK format PED file, and no alleles, like a FAM file in PLINK.