While ancestry.com has a lot of info, much of it is not so good, especially that that is contributed by individual researchers, as opposed to transcriptions of public records. The latter are OK, but you will run into typos, misspellings, and other problems, such as M(ale) mistakenly entered for F(emale), or vice versa. All of it needs to be verified independently, but can be helpful.

You might also try the Mormon site, http://www.familysearch.org/ but it also has problems like the above-mentioned ones. They do no quality control, as I understand it.

The best way to start genealogical research is to go to the oldest members of your family and ask them about their ancestors. Then go to the public and other records to verify and expand. If you or your father know his biological mother well enough, talking to her would be the best place to start. If you don't, you might try Y chromosome DNA testing to see about your father's father's ancestors. True, it is something liek casting your bread upon the water. Family Tree DNA http://www.familytreedna.com has the largest database, and is therefore most likely to have some one with results close to yours. After you receive the results, you can also post them at www.ysearch.org which is open to test results from all the companies.

You could also test your father's mitochondrial DNA, which he inherited from his mother, for some clues as to where to look further, though this isn't used as much in genealogical research as Y chromosome DNA.

If you father's mother was born before 1930, she should be listed in the census for that year at ancestry.com, possibly in her parent's household.

Good luck and happy hunting.