It is best to replace all four tires at the same time. If that is not possible or necessary, replace the two front tires or the two rear tires as a pair. Replacing just one tire can seriously affect your vehicle's handling.

Intuition suggests that since the front tires wore out first and because there is still about half-tread remaining on the rear tires, the new tires should be installed on the front axle. This will provide more traction, and by the time the front tires have worn out for the second time, the rear tires will be worn out too. However in this case, intuition isn't right...and following it can be downright dangerous.

When tires are replaced in pairs in situations like these, the new tires should always be installed on the rear axle and the worn tires moved to the front. The reason is because new tires on the rear axle help the driver more easily maintain control on wet roads because new, deeper treaded tires are more capable of resisting hydroplaning.

...

If the rear tires have more tread depth than the front tires, the front tires will begin to hydroplane and lose traction on wet roads before the rears. This will cause the vehicle to begin to understeer (the vehicle wants to continue driving straight ahead). Understeer is relatively easy to control because releasing the gas pedal will slow the vehicle and help the driver maintain control.

However, if the front tires have more tread depth than the rear tires, the rear tires will begin to hydroplane and lose traction on wet roads before the fronts. This will cause the vehicle to begin to oversteer in which the vehicle wants to spin. Oversteer is far more difficult to control, and in addition to the initial distress felt when the rear of the car starts sliding, quickly releasing the gas pedal in an attempt to slow down may actually make it more difficult for the driver to regain control, possibly causing a complete spinout.