Firstly, you'll need to update your device. The iOS version is now at 3.0, while Android is at 8.0. Android users who aren't seeing the update right away should keep checking back.
Once you have the updated version, launch the app and tap on the profile icon located next to the search bar. Then scroll to the bottom of the page.
There'll you'll find a new section dedicated solely to offline maps. You have two methods for saving a section for offline use. The first is here in the settings, or by typing "OK Maps" into the search bar at any time when viewing a map.
After activating the save dialogue, you're able to zoom in and out of an area and save it to your device. If the area is too large, you'll be asked you zoom in, name the area, and save it.
Keep in mind any saved maps will only remain on your device for 30 days. Presumably, after that the app will purge a saved map to clear up space on your device.
Details from cnet.