I'm not quite sure whether your question is about the dropdown list, or the lookup aspect.

For lookup, as an alternative to khamilton's suggestion you can also use

=VLookup(A1,Sheet1!$A$2:$b$3,2,false)

If you want to learn about dropdown lists, read about data validation here:
http://www.contextures.com/tiptech.html , scroll down to the data validation section and start with the intro.

hth