you can send an intent to the google maps app and have the app do all the work for you but its not documented and probably never will be.
to do that you can either give it a lattitue/longitude like this
Intent NavIntent = new Intent(Intent.ACTION_VIEW, Uri.parse("google.navigation:q=" +latitude +","+longitude));
startActivity(NavIntent);
or using the same intent but with an address and see if maps can resolve the address. (I dont have an example with an address).
Other than using google directions API or other 3rd party direction web services there really is no other way to get directions in your app unless you look at Open Street Maps
where you calculate the directions yourself using way points but that is quite involved