Use software to store and organize information.
Start with what you know. Collect as much information from relatives as you can, then get it organized, preferably with some genealogy software package, before turning to the internet. When you're organized you'll be able to take advantage of what the internet offers.
Evaluate everything you find! Nowhere is the computer adage GIGO (Garbage In, Garbage Out) more true than in online genealogy. Almost all the material must be double checked. Many web genealogies are strings of wishful thinking repeated from other strings of wishful thinking. This includes information from LDS's Ancestral File, FTM's World Family Tree and Ancestry's Ancestry World Tree. Very few online genealogies are documented. Treat online information as hints to guide further research, not material to copy blindly into your genealogy. Follow the advice in Evaluating Web Sources and Standards for Genealogy Research
Don't fire off e-mail with general questions to historical societies, libraries, discussion lists, etc. Many organizations (academic libraries) will not do genealogical research, but will help you use or locate material that is unique to them. Lurk on discussion lists and observe the traffic and how queries are phrased. Often there are specific rules for subject lines.
Don't ignore print resources! Electronic resources are useful portals to information--but often you will still have to order microform, photocopies of records, etc. Many print resources will not appear online for many years. Don't wait!
Good Luck with Your Research!