To copy a singleplayer savegame, you’ll have to first of all locate the directory where you have saved ARK. Usually, that’s
C:\Program Files (x86)\Steam\steamapps\common\ARK
However, if you have selected a different Steam Library during installation it might differ. In that case right-click on the game in your Steam Library, go to “Properties”, click on the “Local Files”-tab and click “Browse Local Files”. That will bring you to the folders for your game.
From now on we will assume that ARK points to your ARK-folder. There are three files that you will have to copy over
Put those into the equivalent directories on your other device, and you’re ready to go!