Since you didn't provide the specifics, I'll make some assumptions.
Table1 has the indexes appearing multiple times. Those index are in column A. The sheet in which Table1 is in is called Sheet1. Column B is where you need data appended from Table2.
Table2 has the indexes appearing only once and they are in column A as well, but the sheet is named Sheet2. The data to be brought into Table1 is in column B.
Both tables have headers, meaning that the actual data starts on row 2.
What you need here is
=VLOOKUP(A2, 'Sheet2'!A:B, 2, FALSE)
VLOOKUP takes the index in A2 and looks it into column A of Sheet2. When a match is found, it will return the contents of the corresponding index from column B, the second column in the selected table array (the table array is A:B).
FALSE indicates an exact match (
TRUE indicates approximate match).
Then you simply have to fill this formula down till the end of Table1.