The first place to start your search for your family heritage is at home.
The first step is to get a notebook. It does not have to be anything fancy, even one costing less than a dollar will do. A three ring binder will allow you to add pages as necessary. You just need a place where you will collect information. Obviously you can use a computer too. Just make sure to back up your work frequently. The more places you store your data the safer it will be. Be careful not to use too public a forum, you don't want to disclose sensitive family information about living or recently deceased persons. A password protected website or private wiki will work.
It is important not to delete anything you have collected, especially when you find contradictory information. Just mark down the discrepancy and investigate it, who knows what family secrets you may reveal...
Start by writing down what you know: your name and birthday, those of your parents, grandparents, siblings, children, cousins etc. No matter how mundane this may seem, it is really the nucleus of your research.
Next ask your family members what they know. What does your father or mother remember about their grandparents? Vital information such as birth, marriage and death dates are very important to research, but don't overlook anecdotes. Stories often lend heart to your project and recording them preserves something that is easily lost to time. Make sure you also get marriage dates and maiden names.
It may seem odd but addresses are another piece or helpful vital information. These are especially useful when you begin to use the census in your research. Ask your living ancestors if they can remember their old addresses and when they lived there. Make sure you write it all down.
Utilizing these very basic resources you will built a solid foundation from which you can take your first steps in genealogical research.