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I haven't used the WiFi shield, but instead used a PCIe Mini Card. I described my experience a bit in my answer on this post
I think this way of doing it is better as you will also have way better performance with things like multiple connections and throughput.
Just my 5 cents.
By default the Galileo will work with the Intel Centrino N135 and N6205
If you install the drivers, you can get the N6235 to work. I have personally done that so I know it works. I followed the instructions in Sergey's blog. Intel Galileo Meets Wireless - Malinov Family Web Presence
In theory, since it is running Linux, any mPCIe card that has a linux driver should work. But I don't think anyone has tried all the various cards yet.