[{quoted}](name=Aziriously OP,realm=NA,application-id=WEuoGbmp,discussion-id=He26KPcX,comment-id=0000,timestamp=2015-01-04T04:43:43.004+0000)
Try to make trades with the enemy, Don't ever let them get free damage on you since it will allow them an easy all in and potential kill shortly.
^^ Mostly this. Never trade unevenly if you can help it (unless of course you are the one who is dealing out more).
Back to Original Poster: Multitasking is kind of an acquired skill that comes with practice, but basically you got to put the minion health bars and what the enemy champions are doing into a kind of dual concentration mode.
Finally standing behind your own minions can help. There are exceptions where it will not, and those are quite plentiful. Some abilities cannot shoot "through" the minion, and therefore it acts as a shield, with it taking the damage instead of you. Supports like Lux, Morgana, Blitzcrank, and Thresh can have their skillshots blown on minions. Supports like Lulu can skill shot "through" the minions. Others are targeted and minion agnostic (Annie, Zilean, Fiddle, etc.).
So don't sell off dodging skills just yet, but many times the minions can help.