I start by looking at the map. I go in the direction of the place I want to be. If I want to know the technically fastest route then I let my device calculate that. I don't always take that route. It's an assistant, not a boss. It's more interesting to walk down different streets sometimes. (And while I'm preaching to Americans, it's also good to walk down streets sometimes. It breaks away a few layers of abstraction that you have when driving.)
Looking at the map actually helps you learn the city layout. As of right now (literally as I'm typing this) the train was delayed, so I chose to get off at the next big station before everyone crowds on, and walk the rest of the way. I can do this without checking a map because I know where it is and where I am, because I don't let the machine think for me.
I don't drive (non-car-worshipping cities are amazing) but I do this when walking and also with train routes. I don't memorize the bus routes, since the train is better and has fewer routes, so I also sometimes ask my device for a route if I think there's a faster bus route than train (usually not the case).
btw on that walk I happened across a store selling lots of varieties of some of the things I wanted - more than the place I was actually going to. Exploring pays off. Randomly.
Looking at the map actually helps you learn the city layout. As of right now (literally as I'm typing this) the train was delayed, so I chose to get off at the next big station before everyone crowds on, and walk the rest of the way. I can do this without checking a map because I know where it is and where I am, because I don't let the machine think for me.
I don't drive (non-car-worshipping cities are amazing) but I do this when walking and also with train routes. I don't memorize the bus routes, since the train is better and has fewer routes, so I also sometimes ask my device for a route if I think there's a faster bus route than train (usually not the case).