1) Record What You Know
You might be surprised what you already know. Write down what you can from memory in a way that makes sense to you. As long as you'll be able to come back to what you wrote in a few weeks and still remember what everything means, you should be okay. The two most standard forms for recording genealogical information are the pedigree chart and the family group sheet. For a pedigree chart, click here. For the family group sheet, click here for the front and here for the back. (Please note that these are the charts as provided by the Church of Jesus Christ of Latter-day Saints and as such have fields for temple ordinances. If you dislike having those fields, a simple Google search should provide a link to a blank form somewhere without them. Or you can make your own. They aren't too difficult.) Using these standard forms (or scribbles that follow their pattern) will probably help you as you go along as you work with others who are using the same forms. Teamwork is a big part of genealogy.
2) See What You Have At Home
Hidden somewhere in your attic (or maybe your parents' and/or grandparents' attics) is a box that will greatly help you on your quest. How do I know this? Because most people have some sort of miscellaneous papers box where they store things that they feel are important enough to keep but aren't sure what to do with yet. Some of these boxes have vital records going back two to three generations. My lucky box was found in the attic of my grandfather's sister whom I have never met, so you can see that sometimes it takes awhile to find "the box." In the mean time, find any document that would prove a vital statistic for a member of your family, which could be any one of the following: birth, marriage, and death certificates; naturalization petitions and certificates; immigration records; military records and awards; land records; wills and other legal documents; passports; family Bibles; etc. Other treasures you may find include newspaper clippings with stories about the family, family pictures, journals, diplomas, and letters. This second set can give evidence to events (don't you think grandma probably wrote letters like mad to tell people that your mother was born?), but usually they are best used to give the information that adds personality to the people you are researching - in short, they are the difference between a genealogy and a family history.
3) Be The Ancestor You Wish You Had
What do I mean by this? It's simple: while you are looking for your lucky box, you'll probably wish that your ancestor had left behind more for you than he did. Some bit of information that he could have rattled off with no difficulty has now become your great hurdle. While collecting the documents that source the lives of your ancestors, also collect the documents that source your own life. While looking for the journals and letters of your family, write your own journal and letters. You (and your descendants) will be glad you did.
4) See What Your Family Members Know
This is the part of beginning research with the greatest amount of urgency. You never know when grandpa or grandma is going to "head to greener pastures," taking what they know of the family with them. Talk to them sooner rather than later. Remember that that far distant great-great-grandfather of yours was your grandmother's grandfather. She probably met him and can tell you things that no document on Earth can. Don't lose that opportunity. Also, don't completely discount things such as email and social networking sites for this step. They may be the best way to keep in touch with cousins both near and distant that could know what you don't. Don't be afraid to ask them for help when you get stuck. Chances are that they are going to be excited to help you (especially if you aren't asking them to do any of the hard work).
5) Make A Record of Everything
You are going to have to record three things:
1) The genealogical information you find (dates, places, relationships)
2) Family stories
3) A detailed log of all of the record types that you have searched and the results of your search.
The next post or three will be covering this step. There are many ways both tech-related and otherwise to accomplish creating a solid record, but what is most important is that you do. Otherwise everything you discover will quickly be lost again.
These steps offer just a basic guide. Every situation is unique, and you may find that as you begin your journey that one of these steps don't apply to you, or you may discover one that I've forgotten. Whatever you do, remember to enjoy yourself. Family history is a life-long pursuit, so don't worry if you don't know everything in the first week. Good luck!