I am TOTALLY interested in this, but not really sure how to go about it?
Here's what I can offer briefly...
1) Talk to your living relatives. Also, gather any existing family trees, family histories, etc. You need to get enough basic information to get you back to people that were born before about 1920. For privacy reasons, not many public records and census data have been released after period of time. Once you get back to that time frame, the availability of records is often wide open.
The more information you have the better. Dates of birth/death, name(s) of spouse(s), where they were born/died, names of siblings, etc. A lot of the dots have to be connected by coincidental evidence. You have to be able to answer questions like "How do I know that this 'James Smith' is MY 'James Smith' in a census record?" The answer may depend on matching things like the name of his wife, when he was born, the names and ages of his kids, etc. The more points you can connect, the more "sure" you can be of ID'ing the guy as "yours".
2) Dates are often "soft". Don't get rattled if an age is off a year or two in a census record for someone you're looking for. For starters, Census data usually only reports their age on the date of the Census. That alone makes the computed year ("They were listed as being 22 in the 1880 Census") only good for an accuracy of +/- 1 year unless you know the month and day of their birth. People also gave census workers bad information on their age, or they may have been mis-transcribed. I have one relative whose birth year swings 10 years across the census records (and his headstone doesn't exactly match any census record either).
3) Be careful. Sites like Ancestry.com and rootsweb allow people to self-publish family trees. They are very useful, but have the same pitfalls as Wikipedia does with its facts. There is BAD data out there. I initially got excited when I found trees published that showed a connection for me with William the Conqueror. I found the links repeated in other trees, but it was all obviously cut-n-paste from the same source. More digging revealed that there was a father and daughter in the linage that were undocumented connections based on little more than a mention by name in a will and an assumption that this meant that they had to be a child of the will's owner. In another example, I also found a published tree that merged two generations of my ancestors into one person (they were a "Sr" and a "Jr") with his mother listed as his wife (ick!)... I contacted the tree's owner and sent them photos of both of their headstones as proof and they corrected their tree.
If you use stuff from other people's trees, make sure it's documented or look for independent confirmation in other people's trees. If the info is just copied and pasted from place to place... be careful.