Google Sheets - How to retrieve a value from a range in one sheet to use in a formula on another sheet?

Try using the following in SheetB!B2:

=HLOOKUP(B$1, SheetA!$A$1:$2, 2, FALSE)*$A2

You'll actually want to use HLOOKUP instead of VLOOKUP, since you're searching a row horizontally instead of a column. You can then drag/copy the formula to all the relevant cells on SheetB.