From your DP table we know f[i][w] = the maximum total value of a subset of items 1..i that has total weight less than or equal to w.
We can use the table itself to restore the optimal packing:
def reconstruct(i, w): # reconstruct subset of items 1..i with weight <= w
# and value f[i][w]
if i == 0:
# base case
return {}
if f[i][w] > f[i-1][w]:
# we have to take item i
return {i} UNION reconstruct(i-1, w - weight_of_item(i))
else:
# we don't need item i
return reconstruct(i-1, w)