Generating a grid such that the elements in each row add up to one

You can use IntegerPartitions, which (despite its name) also partitions rationals. Your problem is to partition the number 1 into a set of $d$ nonnegative integer multiples of step:

d = 3;
step = 1/2;
Flatten[Permutations /@ IntegerPartitions[1, {d}, Range[0, 1, step]], 1]
(* {{1, 0, 0}, {0, 1, 0}, {0, 0, 1}, {1/2, 1/2, 0}, {1/2, 0, 1/2}, {0, 1/2, 1/2}} *)

Permutations makes sure that you get all possible partitions in all $d$ dimensions. You may want to use Sort on the result, depending on use case.

I think you might be looking for something like this.

myGrid[d_, n_] := (#/Total[#] & /@ RandomReal[1., {n, d}])

This should work for number of rows, n, each having d elements. Let's look at a couple of examples.

SeedRandom[1]; g1 = myGrid[3, 2]

{{0.475687, 0.0648416, 0.459471}, {0.379475, 0.487694, 0.132832}}

Total /@ g1

{1., 1.}

SeedRandom[1]; g2 = myGrid[5, 5]

 {{0.380624, 0.0518834, 0.367649, 0.087452, 0.112392}, 
  {0.0339626, 0.280141, 0.119421, 0.204589, 0.361886}, 
  {0.0812216, 0.287062, 0.162136, 0.0948983, 0.374682}, 
  {0.291637, 0.32702, 0.204302, 0.103509, 0.0735315}, 
  {0.274026, 0.0608128, 0.144656, 0.336122, 0.184383}}

Total /@ g2

{1., 1., 1., 1., 1.}