There are some champs that can beat the crap out of you early game. These champs, such as Riven, Gangplank, and Lee sin, are powerful from level 1 to 3 and are near undefeatable in the first five minutes of the game. Well, how are you going to defeat these guys?
First of all, you want to pick a good champ, with good runes and masteries. Things that will boost your health and defense, making you harder to kill. This is pretty easy, all you have to do is set up a rune page with armor yellows, maybe health quints.
But, you may ask me, how is this supposed to help me? Can't the enemy player do the same thing too? Well, it's trure that he can. But if you apply combat multipliers on top of your base stats, you can beat him.
First of all, don't fight the enemy in the middle of the creep wave. Instead, only move forward to last hit, and then walk back to your caster minions. One caster minion does 10~16 dps. Three adds 33 dps. This is a lot early game. A person with 500 hp getting hit by three caster minions will does in 15 seconds.
Next, use the technique of kiting. Learn the attack speed of the champion you are playing, and animation cancel as soon as you hear/see the damage hit. Move in a circle around the ranged minions, Because this kind of movement forces the enemy to move, their attack speed will actually decrease by almost 0.2 sometimes. This is a significant amound of damage, escpecially considering most early game attack speeds are roughly 0.6. Obviously this is easier to do when you are ranged, and is less effective against ranged enemies (but, it still works.)
Finally, you as soon as you get hit by an enemy attack, you can use a potion. An extra 150 health is very useful when you are using these techniques, because these Techniques are all multiplicative. That is to say, they increase in effectiveness the higher your base stats are (hence, have a strong base stat.)
A true master of these techniques will have almost no problems against early game attackers.
Use the creep wave. Kite your enemies.