As you start to build your family tree you will quickly realize that the size grows exponentially. Consider that you have two parents, four grandparents, eight great grandparents, sixteen great great grandparents, etc. Add in siblings, aunts, uncles, cousins and you get into the hundreds of relatives in no time.
With the size of a tree in mind, moving in too many different directions at the same time can easily overwhelm (and possibly discourage) you. I recommend researching one line at a time as you move through the tree. In my project, for example, I have started with my paternal Siragusa line which has allowed me to concentrate on just that surname -- all the way back to the 17th century. Next, I'll work on other branches in the paternal line -- my paternal grandmother's Denny line, my paternal great grandmother's Malatino line, etc. After those lines, I'll move to my maternal lineage. Focus will keep you sane (at least it works for me!)
Accuracy should be a top priority in your family history project. Errors are everywhere! Mistakes in spelling, dates, given names, indexing, and other omissions are commonplace in records of all types. I spent countless hours searching Ellis Island records looking for my great grandfather's arrival in America with no results. When I finally found the record it was indexed under his first name instead of his last. Just because you can't find a record the first time you look does not mean it doesn't exist. Always consider the likelihood of misspellings and think about alternate ways to search.
Always verify your information with primary records (original documents recording an event such as a birth, death, marriage, etc.). Often times it can be tempting to add information obtained from someone else's tree or a family remembrance of a date or name, but make sure it's accurate before committing it to your project. Use these secondary sources as clues, then verify the information with a primary source.
One of the most rewarding aspects of genealogy for me is all the new things you can learn. Whether it's historical information, origins of a name, cultural traditions, or finding new relatives, I seem to learn something new almost every time I work on the project. If you find that you need help, know that there are lots of people that are more than happy to give you a hand or point you in the right direction (not to mention professional help available should you need it). Seek out people in discussion forums (like RootsWeb.com) that are researching similar places or types of records. I also highly recommend that you visit your local Family History Center to access volumes of information and tap into the expertise of the volunteers and patrons you will find there.
www.familysearch.org - FamilySearch is an incredible resource that you can access with no subscription fee. If you are serious about genealogy you will spend a lot of time on this site. I'm constantly amazed by the sheer volume of information that has been collected and presented here by the LDS church. In addition, this is your gateway to a vast amount of microfilm that can be ordered for viewing at your local Family History Center.
www.stevemorse.org - You can call Steve Morse the "king of the search" with his collection of "one-step" web pages. When you need to find an Enumeration District for a census record or want to do a very flexible and detailed search for Ellis Island records, this is the site. Again, a great collection of free tools.
www.ellisisland.org - Here you will find all of the manifests for port of New York passenger records from the late 1800s through the mid 1920s. The site is free, but the search engine can be frustrating at times. If you have no luck with your search, try it through Steve Morse's form (previous site mentioned).
www.ancestry.com - Ancestry is probably the most popular genealogy site, but it does come with a monthly subscription fee. You will find a vast collection of records and user-submitted family trees that may help your search. A word of advice: be careful with the green leaf "hints" -- especially those from other trees. You can easily add someone else's incorrect information to your tree. Always confirm with primary sources.