to play offensively you should choose a high damage champion that will hit very hard but will not be able to take many hits. the champion will be able to have abilities that regenerate health of move to a enemy faster or the ability to give chance and slow or move faster than the enemy champions if you take out their defensive player you could let your minions move up in order to take turret fire. while the minions take the turret fire you need to advance on their turret and attack it and take it out if you can. My personal favorite offensive champion is daydreamer he is a champion with massive attack and a lot of the essentials things that a offensive champion should have. tryandamere's q gives him a lot of his health back his w slows his enemy's so that they cant move so he can use his e in witch he spins fast in a direction either to start a fight by moving in their direction them or getting out of a fight by moving away and his r makes him immune to death for five seconds allowing him to kill a champion while he cant be killed him self.