=vlookup(a2,sheet2!a:b,2)
would be the basic formula.

You may want to read Debra Dalgleish's notes:
http://www.contextures.com/xlFunctions02.html

Wendy wrote:

I have a column of city names in excel FILE A. In the column directly to the
right of the city, I want a formula to lookup from FILE B and enter the
correct county name from another work sheet column.

FILE B contains a column of all the possible city names and a column of
their county names.

I'd be so happy to have some help on this. Thanks.

--

Dave Peterson