Minecraft wiki entry for Nether_survival, associated text: This only works in the Overworld, as water cannot be placed in the Nether, not even long enough to convert lava. Water in a cauldron does not work, and in the End, nether portals do not work at all.
The water does not need to flow over the lava; any lava source block that finds water (source or flowing) next to it gets converted immediately.
Flowing lava converts to cobblestone, and if lava flows into the water it converts the water to stone or cobblestone; if either is inside the frame it must be removed before lighting the portal.
The lava can be carried in as many buckets, but if a lava pool is handy, one or two buckets are required to fetch each block as needed.