Different ways at different times.
Often starting with the number, adding on the tens (by counting in tens if needed) and then adding on the units. So 59, then add 20 either by going straight to 79 if the child knows 5 + 2 is 7, or if not, then by counting 69, 79. Then adding on the 3 units, either counting: 80, 81, 82. Or if slightly more advanced, by adding 1 to make 80, and then adding the other 2 to get to 82.
Other times they will add the tens together, so 50 + 20 to get 70. Then add the units together, 9 + 3 to get 12 (either by knowing that fact by install recall, or by adding on one at a time, or by using number bonds to ten, like adding one to make 10 and then two more to get 12). Then putting the 70 and the 12 together to get 82. (Possibly in stages, if needed, like 70 + 10, and then adding the 2).
Some of them do learn column adding as well, often by labelling the columns with tens and units.