So family history is your new interest and you don't know where to begin; might I suggest hugging a tree. A family tree that is. When I started my first tree I talked to Ma and Pa and found out everything they knew about their Mas and Pas and their Mas and Pas and so forth and things started to come together pretty quick after that, plus there were a lot of other family history researchers in the family that had info on my tree and knowledge is power.
1. INTERVIEWS. The first thing you need to build a family tree is roots. Talk to people who know people. Take notes, literally. I have notebooks full of them.
2. TREES. making your first tree in your notebooks is a start, but eventually you may heed something bigger and more organized. I bought the Family Tree for Dummies package which came with software that is very useful and user friendly. Also, you can get software online at MyHeritage and Ancestry. Oh, yeah and always download the GEDCOM for backup when you are done. You can get a free tree builder at http://www.myheritage.com/family-tree-builder to work on offline or you can make a tree online at Ancestry or Geni or WikiTree of FamilySearch. I recommend using them all. GEDCOMs can be made and downloaded at MyHeritage and Ancestry and Geni and WikiTree too. It doesnt hurt to have more than one...
3. Save your sources and document them. Print them too if you can. Hard copies are always great for scrapbooks...
4. Research. Family history sites like Ancestry and Family Search and My Heritage and Geni can help you find answers to the unanswered questions that pop up from time to time, and it does not hurt to have other researchers working on your lines to consult with. Look for genealogy groups at all your favorite social networks too.
5. Take notes and lots of them. Those notebooks will come in handy later.
Best of luck on your research and happy hunting. Now go grow that tree.