GABA A receptors are acted on by benzodiazepines, for instance.
GABA B receptors are acted on by GHB.
GABA A receptors increase conductance of Cl into the cell creating a larger negative barrier that must be overcome before threshold is reached and an action potential can be transmitted.
GABA B receptors hyperpolarize the cell by allowing K into the cell, preventing Na channels from opening and conducting the signal.
Most of the effects are primarily CNS related, though there are GABA receptors in the periphery I don't think they're there in any appreciable quantity or that supplementing with GABA would have any measurable effect.