How do you get started in genealogy?

My dad was quite interested in family genealogy for the last 35 or so years of his life – maybe longer, but that’s at least the part I’m aware of. He would often share things he had learned. Now, I wish I had paid more attention to it. It’s my understanding that the family has descended from Mayflower passenger Henry Samson. My dad had begun the effort to document that, now, I’d like to figure that out myself. Will I keep it up or lose interest?

Short term, the big question is, “How do I even get started, and where are the resources to do this?”

A quick Google search found lots of links. Here are some to get started: