Hazel...assuming you are trying to locate info on your ancestor including and past the Titanic...
Well, the down side to doing this is that you really need to know the date of arrival and/or the ship name. The reason being is that ships were arriving every day all day.
I was lucky enough to have an old letter from a great aunt who knew the name of the ship that her parents arrived on and the date.
Anyway, it doesn't hurt to give it a try. You might have an okay chance if your ancestor arrived in a minor port.
One place you could start is a library in the city of arrival. I started by going to
www.libraryspot.com. Click on "public libraries" in the yellow column to the left. Click on "public libraries" again in the center of the page. Then look for the state and then city. It will give you the library for that area and an address. Write them explaining what you are seeking and be sure to offer to pay for copying costs. It isn't expensive. The library I wrote to sent me a digitalized copy of the arrival announcement. Many papers were microfilmed and then destroyed.
Some other places that may help in your search:
www.neh.gov/projects/usnp.html (for accessing old newspapers in the US).
www.archives.gov/research_room/genealogy/immigrant_arrivals/passenger_records.html (for descriptions of available passenger arrival records)
Another place to look which will offer a wealth of info are census records. You will have to be a subscribing member of ancestry.com to get to them or you can go to your local FHC (Family History Center) located in a Mormon church in your area and they will send for a microfilmed copy of the census record from Salt Lake. That cost is about $3.25 for a 30-60 loan. There are experienced genealogists there who can help with the search. (who are you looking for? I can look at the census records for you as I am a member of ancestory.com...but I would need the name, city and state of where he lived...I'll get the county on my own).
Census records were taken every ten years. But the records of 1910 to 1930 are the best as they have the dates of arrivals (and sometimes naturalization dates--which usually occurred about 5 years after an arrival) of immigrants. Getting the date of arrival (if they told the truth to the census taker) will at least narrow down your search for port newspaper info. Census records for later years also give the names of the entire family, their relationship to the head of household, if there are any boarders, the address, occupations, any schooling, where parents were born, languages spoken, any identifying marks, how much money they arrived with, who they left behind, etc.
Also, try
www.cyndislist.com. She has been operating an excellent genealogical site for some time. You can find all kinds of information there...and things on ship arrivals too.
As I also mentioned before, see if he applied for Social Security when he came to the US. Go to
www.rootsweb.com and scroll down to Social Security Death Index (SSDI) on the left side. Click it and type in your guys name. You may see several or many people with the same name so you will have to determine which is yours. The bad part is that getting a copy costs $25. It used to be $7 but I guess they caught onto how many people were into genealogy and that they could make a few bucks.
I hope this helps. It's kind of a condensed form of places to search.