Learn to play unlocked. This simply means that when you move your cursor to the edge of the screen, you can scroll around the map.
This allows you to center the camera away from your champion while you play, giving you better vision of your opponents, who may be some distance away from you. Especially when you play against champions with long-range skillshots (lux, blitzcrank and morgana are some of the ones I remember having trouble against before I "got gud"), having the camera unlocked gives you vision of the opponent when you wouldn't otherwise have it. This is very important to become a competent player from the red side.
I bind the lock/unlock key to T, so I can switch back and forth, actually. When I'm running around the map, or jungling, or something, I like to have it locked sometimes, but I'm always ready to unlock at a moment's notice. This also allows me to re-center the camera on my champion by re-locking the camera if
I was looking elsewhere and need to center again.
Better players probably play unlocked all the time, and have a key to center the camera. I have thought about practicing like that for awhile, but haven't done so yet. You might try some custom games when you change settings to get used to them. I know that intermediate bots also sometimes force you to play red side. Practice makes perfect, and good luck!