Something fairly basic and I'm not sure if you have already done this, but if you have elderly relatives it is a good idea to talk to them. They may be able to tell you stories about their own cousins or other more distant relatives. They may be able to confirm if the person/s you found is a relative. Obviously make sure you write down on paper everything they tell you, and be prepared for some inaccuracies or family stories which aren't quite true (intentionally or otherwise).
Groom is right. There are actually many people who aren't interested in family history. Sometimes if there is a scandal people are very reluctant to talk about it, even if it was nothing by today's standards. And you do need to purchase at least some certificates to make sure you are tracing the right family. Even something as simple as seeing a family on a census and presuming that you are looking at parents and their children, can be wrong. I was nearly caught out when all the children in a family I was tracing had a different mother from the one on the census - the father had remarried. Luckily I bought the birth certificate showing the correct mother or I would have gone completely down the wrong track.
Good luck anyway, and just be a bit cautious - do not rush - and back up your research with certificates.
