Lookup up from Sheet 1 in Sheet 2 and display additional value in Sheet 1 when match

I have spent a day reading forums and trying different formulas and have decided it is just time to ask.

Sheet 1 contains over 20000 lines
Sheet 2 contains 9000 lines

Column A in sheet 1 contains values to match in Column A of Sheet 2, they are alphanumeric.
When a match is found, I want the value in column B of Sheet 2 to display in Column B of Sheet 1, next to the matching value in Column A.

It seems so simple to me but I cannot get anything to work.

I appreciate assistance from others. Thank you!