First of all, find out as much as possible. Online records like Family Search dot org, a free genealogy database, are excellent but they aren’t recent. If you can find a name for a great-grandfather and grandmother, and where they lived, you are on your way.
I don’t like the billing practices at Ancestry dot com, they are horrible- recurrent billing, etc., and general dishonesty. Plus the info is available elsewhere for free.
Do you know of an ancestor in the military? Try fold3.
There are census records, so if you have a name and a place, you can check these- it will list the head of the household and the occupants.
There are two main things in genealogy- 1). tracing lines through various ancestors and building a family tree; 2). Getting biographical information on specific people- say, a Revolutionary War soldier, or an engineer, a chemist… or a day-laborer. Court records are useful and interesting.
The further back in history you can trace, the better. It involves a lot of research, but amazing things can be done online now if you know where to look.
For me, it was easy because I have well-known relatives (albeit distant) whose genealogies are well known- being a distant cousin of Obama through the FitzRandolphs of NJ, I can trace back to Charlemagne. I found word-for-word transcripts of court cases from 17th-century Massachusetts through Court Records published and now online through Google Books (Essex Co Mass courts). And for Revolutionary War ancestors, fold3 has Rev War pension applications online (in the 90s, I got these on microfilm at the David Library of the American Revolution in Pennsylvania). I also examined wills and land deeds in the state archives.
The specific research and info can only be determined by your ancestor’s specific cases. If you have a notorious outlaw, newspaper and court records, and he might be mentioned in a book. A doctor, check old medical books and journals at Google books and other online collections.