Hi -
Well the obvious great place to start is Ellis Island. Look at the original manifest very carefully. You can find relationships on both sides of the Atlantic from these. Remember, things are often misspelled.
http://www.ellisisland.org/
The US city archives where people died can also be very helpful. Remember a city death record is a primary (trustworthy) source for info related to death, but secondary (untrustworthy) for births, etc..... but it provides you with clues, as do obituaries, which are on microfiche in libraries. Many obits have found their way online. And some cities or counties have put loads of original source records online, like Shelby TN. Others, tell you to write and enclose a check. I had a relative who died in a TB sanitarium. I just picked up the phone and called to verify the place and determine the date. A few days later they mailed me her death record with all sorts of information. I didn't even ask.
Marriage records, as well as birth records, from city archives are also fascinating. And WWII military records are nice primary sources, as are any license application.
SSDI is also helpful.... but not 100% trustworthy.
http://ssdi.rootsweb.ancestry.com/
Then there are the regional LDS libraries. Like in Ancestry, look for source material rather than derivatives which can be riddled with errors.
Family Search, with which you may already be familiar, is very good, too.
http://pilot.familysearch.org/recordsea ... html#start
If you have an unusual name, use an online phone book and see if you find a person with that name in that locale who could be a descendant. Write. Of course, be prepared to identify yourself really well so that they don't think it's a scam. Offer them information to confirm your identity & relationship. See if you know a relative who also knows them.
The #1 RIGHT thing to do is to document your sources. #2 - don't publicly share DOB about anyone living, or publicly publish anything you aren't 98% sure of. #3 Admit humility. We all make mistakes.