I'm booting the Galileo board with the SD-Card Linux Image provided by Intel
There is more than one version - which image did you take?
sudo apt-get install does not work for the Galileo.
Indeed. There is also a Debian image out which should support apt-get. However, if you use one of the Yocto Linux images you will have *.ipk rather than *.deb packages. Rather than "apt-get" you would use "opkg". Dependent on which image you installed you might have to specify a repository in "/etc/opkg/" folder if available.