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First, keep in mind that the DRV8835 is not listed in the Shield Testing Report http://www.intel.com/content/www/us/en/support/boards-and-kits/000020775.html , this means that this specific shield hasn’t been tested with the Galileo so there’s no guarantee it’ll work.
Now, we haven’t tested this shield ourselves, but, the physical connection to the Galileo should pretty much be the same as for the Arduino, since both board use the same header pin arrangements.
Now, in regards on how to power the shield I found this very useful guide https://www.pololu.com/product/2511 . It’ll show you an overview of the shield, how to assemble it and connect it to the Galileo and how to use the shield.
One thing that’s important to mention is how you power the shield, there’s a warning note you should read carefully:
Warning: When powering the Arduino from the motor shield, you must never connect a different power supply to the Arduino’s VIN pin or plug a power supply into the Arduino’s power jack, as doing so will create a short between the shield’s power supply and the Arduino’s power supply that could permanently damage both the Arduino and the motor shield. In this case, it is also important that your shield power supply is an acceptable voltage for your Arduino, so the full shield operating voltage range of 1.5 V to 11 V probably will not be available. For example, the recommended operating voltage of the Arduino Uno is 7 – 12 V.
This note talks about the Arduino, but the key concepts on how to power should still apply for the Galileo.
Read the link with instructions we provided and let us know if this answers your questions.