Lookup cell contents on another workbook and replace if found

I have a workbook with a worksheet that contains multiple rows and columns with text. What I would like to do is run a script that will:

1. try to match the contents of the cell with column A of MATCH worksheet on a different workbook
2. If the item has a match (lets say it matches A31), then replace that cell's content with B31 from the MATCH worksheet.

The copy should be value only - no formatting, etc. The MATCH worksheet could also just be a text file if that makes things easier.

Thanks xladept. That was what I was looking for. I was unsure if the better method was using dictionary objects, but this works fine. With slight modifications, I prompt for the both workbooks and worksheets.