You might want to try the keyboard shortcuts that let you snap windows to either side. Just hit ALT+] to snap to the right side of the screen. ALT+[ will snap it to the left side.
If you have a split screen with 2 windows and you move the cursor to the dividing line between the two windows then let it sit there for a few seconds, a rectangular box with 2 arrows will pop up. By dragging the rectangle left or right, you can use this to resize both windows at the same time instead of pulling one windows over the top of the other when you resize them.