There's a setting in windows for mouse movement (control panel -> hardware/devices -> mouse properties -> pointer options) called "Enhance pointer precision," by default this is turned on. If it is turned on, turn it off. In the short run this will feel very strange and you'll often find the mouse either doesn't move as far as you want when you want to cross the screen and will have difficulty moving short distances with precision, but in the long run you can achieve higher precision.
The game contains some features that you may like to take advantage of. Simple right-clicking is usually bound to attack or move depending on whether you click an attackable target or the ground, meaning that if you miss and click the ground you could end up walking towards an enemy instead of attacking them which is often really really bad. Attack-move (shift+right-click by default, I believe) instead has your champion walk in a direction until they find an enemy within auto range and then immediately begin auto attacking, this is a much safer way to safely auto attack at the right distance and gives you more leeway. There is an option that also allows attack-move to direct auto attacks towards the enemy closest to your cursor at the time you clicked IF the enemy was inside your auto range at the time of the click for further leeway for precisely attacking targets.
The next big problem you run into would be attack-moving when there are minions in the way or many minions around enemy champions, causing your auto attacks to be directed at minions instead of champions. There is a 'target only champions' button in the game which only works specifically for attack clicks meaning you need to directly click on the champion without missing. I don't really use that button since I can't find a good binding for it.
Practice always helps no matter the settings you pick.