Either through no fault of your own, or deemed necessary by yourself, sometimes enemy minion waves will progress past the half-way mark of your lane and start milling around your tower. Last hitting under a tower can be tricky. For melee minions, wait for the tower to attack them twice then hit them for the kill with a skill, or an auto attack if you're strong enough. For ranged minions, hit them once, let the tower attack them, and then land the killing blow. This course of action can differ among champions, and you must also calculate the amount of damage your own minions are doing, but the principle remains the same.
Note: Minion survivability scales with time, so you may have to adjust your last-hitting as the game progresses.