I just tried to ssh into my Galileo, and it worked straight away- heres what I did;
(I'm using a Centrino mPCIe wifi card- if you're using a direct ethernet connection then you can skip step 1)
1. upload the 'Connect with WPA' WiFi example sketch
2. once you're connected to your WiFi network, upload another sketch with these two lines in the 'loop' function;
( don't worry, the network connection will persist even after you've uploaded a new sketch)
system("ifconfig > /dev/ttyGS0");
delay(2000);
and open up the Serial Monitor to see the results. We're looking for an IP address- mine is called 'wlan0 inet addr', if you're using ethernet it'll be 'eth0'.
3. open puTTY, or another terminal emulator or SSH client, and connect to 'root@192.168.15.4' on port 22 (replace IP address with the one you got from step 2), and viola!