From the Atlanta airport, you'll take I-85 North...., I-85 and I-75 converge about 3 miles north of the airport, and remain joined through downtown. about 2-3 miles north of downtown, I-85 and I-75 split apart. Take I-75 north... and be careful. Even though I-75 goes northwest, stay to the right as you approach the splitting of the interstates. I-75 splits off to the right, then crosses back under I-85 (I-85 goes northeast).
About 6-7 miles north of the split, you'll approach I-285. Take I-285 west, then immediately get off at 41 (Cobb Parkway). Turn left on 41, and go up the hill. Galleria is on the left... across 41 from Cumberland Mall.
There's a brand new exit immediately before 285 that *might* be a slightly more direct route, but I haven't explored that yet, so I can't promise anything.