Regarding how to connect to the Galileo using SSH, if you're not using the complete Yocto image, I think setting up some things from the Linux side would be a little simpler.
I believe all you would need to do is to set up the Ethernet connectivity, so I recommend you to read this document: 15 Useful "ifconfig" Commands to Configure Network Interface in Linux, and then you could use PuTTY (or some other similar software) to connect to the Galileo using its eth0 IP address.
But what are you trying to achieve?
I think the Ethernet Connectivity is already there as I am able to connect through telnet via Ethernet cable.
The problem is I want to check if SSH is up and running as I can't connect through it.
I saw the link you said and it does not have anything to check SSH status.
I just remembered that SSH is not included in the on-board image, as you said you can connect through telnet with the on board image, but if you want to use SSH you'll need to use the complete Yocto image.
I just tried it and I simply booted from the SD Card, the Ethernet connection assigned an IP address to my Galileo, I checked it using the ifconfig command, opened PuTTY, pasted the IP address and that got me connected through SSH to my Galileo.