As with any hobby, you can go from frugal to freakin expensive pretty easily. I know some genealogists who have subscriptions to every genealogy service, spend quite a bit on DNA tests, acquire tons of records which cost money if you are ordering them from county agencies, and travel back to the home country to do research (think Scotland or England). But the basics of genealogy (tracing your family roots) can be started for free of for very little money.
There are a lot of ways to "do genealogy" but the most basic way to get started is to write down your information (full name, date of birth, place of birth, parent's names, etc). Next, do the same for your parents (full name at birth, married name, date/place of birth, wedding location/date, date/place of death, list of their children, their parent's names), ad infinitum. Of course, genealogy is all about the "proof" which means you need the documentation to prove the information you are writing down (birth certificates showing both parent's names, photos of grave markers, death certificates, marriage certificates, census records, etc).
Fortunately a lot of the basic information you need can be had for free or very cheap. For yourself and immediate relatives you can often ask for copies of records. When you get back generations, you will need to find the records yourself through research (ie: you know that great grandma died in Michigan so you go to Seeking Michigan online digital archives and look for a death certificate which often has additional information on it including date and place of birth, parent's name, date/location/cause of death, etc). Needless to say you can go pretty far down the rabbit hole with this sort of hobby. With some ancestors a simple Google search turns up even more information (one of my ancestors, Mary Staples, was reportedly a witch, another ancestor, Jane Strope, was captured by Indians).
If you want to get started with the fascinating hobby of genealogy, here are some free resources:
- Gramps (a free computer program to record all of your genealogy research)
- Family Search (free genealogy records search database)
- Find a Grave (huge collection of grave information)
- Reddit Genealogy (bulletin board to ask for help and information)
- 50 Free Genealogy websites (all kinds of free resources)
- Finding Your Roots (fascinating PBS show about genealogy)
- List of US Archives and Genealogy Libraries (free libraries to help with your genealogy research)
- Google (often Googling a name and date will pull up info on an ancestor)