How does an aircraft turn while taxiing?
Primarily steering is accomplished in two main ways:


Steerable nosewheels - Usually limited to tricycle undercarriage, and usually controlled using the same left/right pedals as control the rudder in flight
Using the rudder itself - Often associated with the traditional undercarriage (tail draggers to some). In this case the rudder works on the ground in much the same way as it does in the air - ie, deflecting the rudder pushes the tail in the opposite direction, thus causing the nose to pivot in the required direction.


In addition, steering can be augmented in two ways


Differential braking - often the left and right main undercarriage have their own deferentially controlled brakes. These are usually controlled by "hats" on the top of each rudder pedal. By applying greater braking pressure to, for example, the left wheel will cause the aircraft to pivot more around that wheel causing a left-turning tendency. 
Differential thrust - in a similar vane to above, greater thrust applied to the left engine will cause a  right turning tendency.