I've only recently done research into my family, and haven't gotten as far back as I'd like, but this is where I started:

Talk to living family members. Typically ones older than yourself, or ones that have studied your family geneology.

Find documents currently in your family's possession. I found a big box full of photos and documents that really shed some light on my family. For instance, I always thought I didn't have any ancestors in the USA until after the Civil War, but I've found out that my great-great-great grandpa moved from Canada to the US and took part in Sherman's March to the Sea. Also, his name was Hollingshead, the same as Raphael Hollingshead (or Holinshed, depending on the source), who wrote the Chronicle of England, Scotland, and Wales, which was one of Shakespeare's main sources for his history plays. So now I'm trying to figure out how my family made it from England to Canada, and from there whether or not I'm related in some distant way to Rapael H.