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]

Additional question 1) 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]}]

Additional question 2) A blue variable means it is unbound to a value. The variable will be used as a symbol instead. Teal color means it is bound to a value via an enclosing function. In your example, `Sum` binds `i` to a value it fills in. A black variable has a globally assigned value.