You don't. It is not possible to install a four prong outlet using only three wires either legally or safely. Put the three prong outlet back and install a new three-prong cord on the dryer.
As it sits, without any ground to the dryer, there is no way for a ground fault on the dryer (inadvertent connection of a hot wire to the frame of the dryer) to trip the dryer breaker. If it ever happens, the dryer will become energized, and will shock anyone touching it, as well as any form of ground (such as the washer) at the same time. It can also cause a fire.
There are very good reasons for having a ground wire in a circuit, and your new dryer is designed for just such a feature. Without it, the primary safety feature of the entire circuit is missing. Replace the three-prong outlet and follow the link in the article for instructions on installing a three prong cord onto the dryer; this will provide nearly the same safety factor as having a ground wire.