For years I've been collecting certificates and information about ancestors, but it wasn't until recently I started putting it all together. I'm fortunate that on both my mother's and father's side of the family I have cousins who have done extensive research and I have a lot of information from them, but it can become an expensive hobby.
Start by asking relatives for information and ask for any birth, death, marriage certificates they might have. A few years ago, I asked some of my older relatives if they would write one or two pages about their childhood and about family which gave me a look into their lives at the time (and a few scandals).
There are also several places online where you can access information without paying (Wikitree is a good one). Apart from several aunts, I am the first one in my family to move to another country so all my ancestors lived in Scotland or England and my research is a little different from those who may have traveled to the U.S. by boat.
Keep a notebook and make a list of information/dates you are missing.
Once you have as much information as you can gather, sign up for the 14 day free trial on Ancestry.Com. If you start inputting information you will get tips that will help you. Also, many members have copies of census pages which you can download/copy without having to pay an additional fee.
I have found Family Historian a good program to store data and isn't overly expensive, but the charts aren't that great to print and frame.
Also consider a scrapbook to house your memories from relatives and certificates/census pages. At least if you ever lose access to your data you will have it in print.
Have fun and enjoy getting to know some of your long lost cousins. I found someone in a country on the other side of the world who has connections with my family just by doing a Google search for a relative with an unusual name.