"to" or "-ing"

I'm sorry about the confusing subject but I honestly don't know anything about grammar (and the terms used to teach/explain something it). My friend just asked me whether she can use "start to work" or "start working" (which I know you can use both but I don't know why) and I remember there was some list of these verbs (begin, start, love, like, allow, enjoy...) you can use with "to" and those you can use with both or "ing" only. The question is where do I find this list and what is this whole thing called. Thanks for any responses...