After the horse is trained to respond to the leg and rein aids, often all the rider needs is to sit slightly harder on the seat bone that is on the side that you wish the horse to move to. The horse will move that way to stay in balance with the rider - weighting the stirrup on that side may have the same effect but the stirrup is not needed, only the rider's weight in the saddle. Often I see riders inadvertently sitting unevenly in the saddle, sometimes just because the rider is built a little crooked, maybe one leg is longer than the other, or the rider's spine is slightly crooked, and they have problems with a horse drifting in or out, or problems getting a right or left canter lead. Sometimes perceived problems with a horse are really problems with the rider.
What doesn't work to get a horse to go sideways is pulling the horse's head around to the side you want him to move to. Works better to move both reins together in the direction you want the horse to move, so to go sideways left, the right rein will rest on the horse's neck and the left rein will not pull the horse's head around but will hover next to the horse's neck, creating an opening for the horse to move into.