I have been doing genealogy since 1994.
Start by printing out some blank charts that you can find online.
http://www.genealogysearch.org/free/forms.html
You want group sheets and an ancestor chart (pedigree, family tree)
Fill in the information for yourself, your parents, your grandparents, etc. I like to fill in the information I don't know for sure in red so I know to confirm it later.
You then fill in the blanks. Sources are family members, Bibles, diaries, backs of photographs, going to the historical/genealogical section of your library or museum, clerks office for death, marriage and birth records (death and marriage records are open, birth records are covered by the privacy act so most records since 1900 can't be viewed), find an LDS library near you (they have some of those birth records from 1900-1920 that you might not find elsewhere), check for census records (they list names, ages, occupations and much more), state ran libraries are full of records as are college and university libraries, newspapers on microfilm...
Basically you follow a paper trail. It'll lead you from town to town, state to state, country to country. I learned by asking for help at each library. You can also call your local historical/genealogical society to find someone who volunteers their time to get people started. If they charge, it may be worth the money, especially since they know where they keep the obit and family files and know the libraries by heart.
Ancestry.com has a message board that is free. You can post a question per surname or location. Use the search feature often and make sure your subject line doesn't simply say 'help' - post the name or a short version of your question in the subject line - you'll attract more help. Use an email addy with this board you might have years down the road. Just last week I got a response to a 5 year old post. You might find out that someone is searching for the same person so Yahoo/Google search the people you are looking for.
Document your sources very well. If you find a discrepency, you can decide which is a more reliable source, or if you need to go back to that record, you know where you got it from.