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Let's face it, everyone has occasion to run away.
Here are some helpful hints for noobs who find themselves running.
There are also some non-running hints at the end.
1. Utilize the brush. Champions with ranged stuns or slows can't target you if they can't see you.
2. Don't run straight down the lane unless you have some lead. If the enemy is right on top of you then running right down the lane gives them line of sight the entire way so unless you have some crazy movement speed or still have most of your health then you're probably sunk.
3. Change direction. Running into brush while a bunch of people are coming after you and then running back the way you came just as they enter the brush is a really great way to confuse them. Once you pick a direction enemies usually expect you to stick with it. Suddenly running right past them while they enter brush will give you a lead since they will be looking in the wrong direction. This is especially true when the enemy feels that they have the clear advantage. If the enemy is getting overconfident they won't expect to be outsmarted.
4. Keep your distance. If you are facing a champion with a grab, like Blitzcrank or Singed, or facing a champion with a teleport, like Katarina or Shaco, it's a good idea to keep your distance. If you are sure you can beat Singed under a tower then feel free to let him fling you but in general patience will overcome greed.
5. Stay away from people with their ult on. Sometimes it's unavoidable in team fights but if you are laneing there is no reason to face someone with an ult active that gives them a buff, like Renekton or Nasus.
6. Avoid fighting near an enemy tower. I can't tell you how many times my team had the advantage and we all got together, faced the enemy near a tower and died. It isn't so much that the tower did damage to us, most of the time the tower never did damage to us. The mere proximity of the tower gives the enemy a zone where they can retreat, regroup, and attack from. It's better to pull back and wait for a better opportunity rather than trying to push a tower with three enemy champions under it.
7. Intimidation. I like to go mid lane with Cho'Gath because squishy ranged DPS can't kill me early and as a result they are intimidated. I can farm minions without being harassed because the enemy doesn't attack me directly despite the fact that they are ranged and I'm not. This is not always the case with more experienced players but even with them I can hold the lane because they won't come near the tower. Using offensive summoner spells like ignite and exhaust work well with this strategy. For some reason using ignite makes people run away even if your champion doesn't touch them.