Where to begin?
When you start your research, decide who you want to start from. Are you going to do all the family lines? Or just do one side for now? I am working on both my mother's and my father's sides of the family. Very time consuming and very confusing at the beginning of my internet research. If you are just starting out. I would recommend you start one line, and work from the person born on that side. Lets say you want to start on your mother's side. Start your tree from her.
Talk to any living relatives and write everything down. Get copies of important records to work from. It will make things easier as you go. Write or record stories that you can gather facts from and to have for future generations.
Draw up a tree with branches, and put in your family names that you know of, so you have are reference point. Organize your files to keep family members in order. I use several systems, but you may find one that is better for you. I keep a five section notebook, with tabs, that have surnames for the families that I am looking for. I also have an online tree to reference to if I need it. I like my notebook more though. Its handy, I can just reach into my drawer and there it is. I also keep several folders for my census records, one for each branch. Makes it easier for me to figure out where my ancestors lived and where to look for more information.
Never assume the information you find on the internet is true. Always look for references to where the information came from. Confirm facts with a second source if possible. Look for marriage records, birth records, death records. Check the census records to see where your ancestors lived. Try to have two references for every fact you find. Whatever you gather other people may want to use, so you want your research to be correct.
Try to have fun with your new hobby. If it gets to frustrating, than its time for a break.