If you are switching it to another iOS device, then use the following instructions. If you are switching to a device that is not iOS (Android, etc.) then there is no way of doing that, because iOS is separated from android, and you have to completely restart the game on your new device.
First step, login to your Madden Mobile account on your device that you are currently using, before you switched. Once logged in, go in to the settings on your old device, and select the "Recovery Code" option. Keep this code to yourself, as anybody that knows this can easily take your account. Now that you have the recovery, get it written down or memorized, and open up Madden Mobile on your new device. When you get the opportunity to login to your account on your new device, select "Recover Account" and there will be a place to insert the code into. Write the recovery code from your old device into that place, and you will be logged in to your account from your old device.
Hope this helps!