Navigation and Routing application

I am trying to make a map navigation system like mapquest where you can type in a start address and an end address and have it display the route and calculate the distance and time.
Could OpenStreetMaps do this for me? If so, how could I get started? Sorry if I sound ignorant to this topic as it is new to me.
Thanks for any help.

There are already a number of applications/services that can do this for you:

Most notably: and