DH and I have done a bunch of this. If you are close to one of the National Archives
they are fun to search through although all those microfiche..
many libraries and LDS churches also have info.
Although you should not limit yourself to internet searches because not all info is on the web yet you can get an amazing amount of info and it's a good place to start.
I found most of my info at these two sites;
These are also good place to learn and see what's out there.
You can get a limited amount of info from the pay sites without paying, but my dad got a lot when he did fork over the money.
To get started get as much of this as you can;
Full names, siblings, children, etc..
Birth dates and places
Death dates and places
Marriage and divorce dates and places
Anything you can think of..write down..
TALK to family members and write down everything they know or "think" they know..it may come in handy. Be aware that misspellings are common especially on those old handwritten census records, and names were often changed or misspelled during trips through Ellis Island or wherever.
To give you some idea what can be found..
DH was looking for a connection to Mary Todd Lincoln. We went to the National Archives, libraries and LDS churches before the internet and found a lot of stuff, but we got stuck at one point. We had the name S.S. Todd in Santa Rosa, CA, but couldn't seem to get further. Because of the time frame DH started searching the internet for civil war info and all of a sudden he yelped..he came up with a possible name. Going from that I ended up finding a relationship to other names we had! We've now gone back to the Revolutionary War and found out our daughters are eligible for the DAR if the should be interested some day. Amazing! Oh! I should also mention that we made the Mary Todd Lincoln connection.
I have gotten back to about 1800 when family came over from Luxembourg and I can't seem to get further, but it's been interesting.
This what you're looking for?