Create lists like this:
g = {1, 2, 3, 4}
h = {10, 20, 30, 40}
Then you can sum like this:
Sum[g[[i]] h[[i]], {i, Length[g]}]
or more nicely (Mathematica does element-wise operations automatically where applicable):
Total[g*h]
You can use this feature to easily calculate a new list with the results, without using indices:
f = (g h)/Total[g h]
{1/30, 2/15, 3/10, 8/15}
If you want to use indices anyway, you can do it with Table:
f1 = Table[
(g[[k]] h[[k]])/Sum[g[[i]] h[[i]], {i, Length[g]}],
{k, Length[g]}]