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