You are very close with your formula.
Use:
=VLOOKUP(A2,Sheet1!$A$2:$B$99999,2,FALSE)
Your reference to Sheet2!B1:B999
should be Sheet1!$A$2:$B$99999
. Your original is actually pointing to the place where you want to put the results, not the source of the numbers.
The Vlookup() function needs:
What you are looking for - A2
Where you want to look - Sheet1!$A2:$B99999 (your look up table)
What you want to return - 2 (the second column of your table)
If you want a close but not exact match - False
By putting the $ in the range $A$2:$B$99999, the reference to the table will be fixed. So when you copy the formula down through the rest of the cells, the look up table range will not change.