My answer may not be best suited for you but I'll explain what I did to kick start my research.

I started from nothing. All I had were a few stories and my grandparents were both deceased when I started. I knew roughly around when my grandparents arrived in the US so I started searching Ancestry.com. This is where I got my start. I was able to find out their SSNs, the ship manifest that they were on and some other related information of their time in the US. This was what I used to search US Immigration records and was able to obtain my grandparents' A-Files. This ended up being exactly what I needed to start exploring for information outside of the US.

As it turns out, my aunt actually had my grandfather's birth certificate in her possession, she just failed to ever look for anything over the many years I kept asking. This actually gave me accurate town names and his parents' info.

Depending on what country you are from, I would start locally. Gather what information you have on them (what towns they lived in, etc) and also send requests to US Immigration.
http://www.uscis.gov/portal/site/uscis/ ... 18190aRCRD

Good luck!