To connect to the CSIL machines from Linux, you just use the ssh command at command line.

ssh username@csil.cs.ucsb.edu

If you are using an X11 desktop, you may find it helpful to use one of these so that you can access graphic programs on your Linux machine:

ssh -X username@csil.cs.ucsb.edu

or

ssh -Y username@csil.cs.ucsb.edu