Once you have gathered information on a couple generations in your family tree, you may want to look into genealogy software to organize your information. Software can vary widely in features and price. Basic programs allow input of names, dates and locations, but little else. More advanced programs allow you to add photographs or other documents, note sources of information and more.
The number of features is not always a good indicator of price. I currently use MyHeritage's Family Tree Builder. It is a free version with the option of upgrading to the premium version. However, even as a free version, it offers quite a bit. One of the features is SmartMatching. The software looks through other family trees made with their software to see if there are any matches. The premium version offers better matching, but I've had some success with the matches provided with the free version.
This is only one of the several free genealogy programs available for family tree researchers. I will be researching the other options and reviewing them in the near future.