I accidentaly uninstalled the game from my phone. How can I get my account back?

If you bound the game to an external account then you can get it back easily. If you did not then the only way to retrieve it is to ask the game support for help.

Start a new game, you will need to play through the initial tutorial steps, once you can access the menu open the Settings menu and tap on the Account option. Here you will have the option to 'switch account' if you have log in details for you previously bound game. If not then look for the link to 'Retrieve lost account' (at the bottom) which will let you send the details of the old game to the game support.