Populate cell from 2 columns

Is it possible to populate a cell, by comparing another cell with a column, with information from a different column?

I have been trying to use the IF functions but must be overlooking something. I have 2 sheets setup, I want to pull 1 column from sheet 2, compare it with a cell on sheet 1 then populate a different cell on sheet 1 with a value from a 2nd column on sheet 2, the data to populate would be in the same row as the data taken from the 1st column. Basically I want to change the value in a cell on sheet 1 and have the other cell automatically update with the matching value from sheet 2. So if I change A1 to match sheet2.A2, B1 updates to sheet2.B2 and if I change A1 to match sheet2.A248, B1 automatically changes to match sheet2.B248.

The best I have gotten so far is running it as an Array, but I don’t want all the values of the column, just the value that matches the data in the other column.

IF(A1=$Sheet2.A:A, $Sheet2.B:B)
=VLOOKUP(A1 ; $Sheet2.$A$1:$B$10000 ; 2 ; 0 )