Depends. If the old phone is working, and you can access it, then you can either upload the files from the old phone to a google account, over WiFi works if the old phone doesn't have regular service, and then download them from said account to the other phone. You can also connect the old phone to a computer via USB cord and move all the files over to an empty folder on the computer. Then disconnect the old phone and connect the new phone to the computer via USB cord. Then copy or move the files over to the new device.
NOTE: These will work with files, they will not work with apps. Apps you have to download and install on the new device directly from their location online (like google play store).
Now if the old phone isn't working, then you can't access any of the files until it is working.