Downloading maps is far simpler than the old convoluted process. You either search by city, state, zip or select a point on the map, then click "Download." It'll bring up a map for you to decide the exact area you want to download, which can be as small as a single neighborhood up to an area roughly half the size of Washington State. Unlike in the past, there's apparently no discernible difference between offline and online modes.
Once you've got an area saved locally, you can do a lot with it. You can get turn-by-turn driving directions, search for business information and destinations, all offline. If your connection gets spotty, the app will seamlessly transition between online and offline modes -- the same way that Google Play Music doesn't really differentiate between downloaded and streaming tracks.
Once your phone finds a steady mobile or Wi-Fi connection, it will automatically switch back to online mode. The initial rollout will only be for the Android version, however, iOS users can still download basic offline maps, and Google is hard at work adding the same functionality to its iOS app as well.