Tip 1: Start in a more athletic stance - a slight bend in the knees and at the waist.
Tip 2: Bend both knees equally. On the mound, this will cause you to lean toward home plate but that imbalance sort of gives you a head start. Many pitchers bend the back leg and straighten the front leg to orient themselves vertically relative to flat ground. But you’re not going to move horizontally - you’ve going to move downhill so orient yourself relative to that downhill direction.
Tip 3: Practice pushing the hips sideways. There is a drill called the Hershiser Drill you can do. You basically stand next to a chain link fence or padded wall, lift your knee, and stride into the fence/wall by pushing your hips sideways. Your hip (or maybe a little bit of your back pocket) should be the first part of your body to touch the fence/wall. Search this site for more details on the drill.