Extremely easy - and very inexpensive. There's also the Indian trains website which will give you the schedule.
It's a pleasant journey, you see some nice countryside.
Beware the "official" tourist guides with badges around their necks who will chat to you on the train and try to steer you into their office when you arrive in Galle. They will then try to load you into one of their "official government" TukTuks to go sightsee, at really ripoff prices. I fell for it.
Galle is a really worthwhile trip - go for it!

Sorry - just realised I said Indian trains - I go there often as well so hence the mistake.
You should look at the Sri Lankan trains website
Go to
http://www.railway.gov.lk/index.php

Or just google Sri Lankan trains for lots of helpful advice.