yes, that's about it. Three long plastic tubes, which water but not soil can get into, in shallow trenches, from three corners of the garden (the dampest corners), all coming into a holding tank at the lower end of the garden near the house.
From there a single pipe leads into the main drain. (There was a drain already; the problem was that it was a couple of inches higher than all the paving, so there was a couple of inches of water lying everwhere after rain). A pump to take it from the holding tank to the drain; it's switched on permanently but only triggered when the water reaches a certain level.