  We give a simple form of the evolution equation and a scalar Lax pair for the
$q$-Garnier system. Some reductions to the $q$-Painlev\'e equations and the
autonomous case as a generalized QRT system are discussed. Using two kinds of
Pad\'e problems on differential grid and $q$-grid, we derive some special
solutions of the $q$-Garnier system in terms of the $q$-Appell Lauricella
function and the generalized $q$-hypergeometric function.
