Being able to understand how turrets, monsters and minions work. Why do opponent turrets and minions hit you and how to avoid them from hitting you?
Towers can only hit you if you are in there range, towers have a vary long range auto attack range and you will not be able to hit the opponent tower unless you get in it. To safely get in range of a tower to hit it you first need minions to tank the tower hits, once minions push to the enemy turret and get in range of the turret the opponent tower will start hitting/killing the minions and will continue killing your minions until there are no more left in its range to kill. As long as you don't hit an enemy champion under the opponent tower and have ally minions under it with you the opponent tower will not hit you, if you do hit the enemy champion under his or her turret it will start targeting you, all you have to do in that case is run out of the towers range then you can go back in if you still have ally minions under the opponent tower.
Minions are similar to towers, a opponent minion will only hit you if you are the first target they (see/run into) and if you hit an opponent champion in their range they will start hitting you but the same goes for them. Although minions don't do as much as towers they still hurt you and in the early game phase of things they can cost you the fight if you are not careful. As a melee champion be careful when your opponent has more minions than you because your opponent may/will out damage you thanks you the minion advantage, if this is happening then let them push you back to your tower and "farm" under tower.
Monsters will only start attacking when someone hits them, when hit it will start running at the closes champion to it and start attacking the champion. Monster will only run so far till they go back to their original place, then they do run back to where they start gaining all their health back till they get to where they started. To minimize the damage you take from killing monsters in the jungle as a melee you can hit them then run back till you can hit them again making it so they are running at you instead of hitting you the whole time, as a ranged champion you can do the same thing just make sure you don't run out of the monsters range because all your work will go to waste as it gains all its health back.
A good player will be able to understand how towers and minions work a great player will be able to use it to their advantage, when under your own tower fighting the opponents becomes much safer because you have a tower helping you if they hit you. If you have any "cc" keep it for then the tower start hitting them to maximise the damage they take from the tower, this also applies to when you have more ally minions then your opponent. Also if you do end up "tower diving" your opponent the tower will start hitting the first person that hits the opponent champion and will continue till he or she is dead or runs out of the tower range.
Note: This is a basic understanding of how turrets, minions and monsters work and there are more details i was not able to cover in this (text), like the different types of minions/towers and more advanced tricks of how to use towers/ minions to your advantage.