To do a general database search, begin with simple keyword terms, like "immigrant" or "immigration." To narrow your results, use Boolean logic to combine terms. By searching for "aliens labor," you are likely to increase the precision of your search, while adding an operator and synonymous terms will increase its recall.
Also, be sure to use the language of the time period you're researching. For example, keyword searches like "alien" or "foreigner" might bring back results that "immigrant" missed. Of course, you won't always be familiar with contemporary language, which is why it's helpful to keep a record of vocabulary as you discover it in the articles you read.
Finally, try variant spellings and variant forms. For example, "immigrant" or "emigrant."