You may pull (download) files from the device by executing the following command:
adb pull <remote> <local>
For example:
adb pull /sdcard/ ~/
You may also push (upload) files from your computer to the device:
adb push <local> <remote>
For example:
adb push ~/image.jpg /sdcard/
Example to Retrieve Database from device
sudo adb -d shell "run-as com.example.name cat /data/da/com.example.name /databases/DATABASE_NAME > /sdcard/file