Up to 23 blocks wide and 23 blocks tall. The minimum is 4 by 5. Anything in between works, and the corners are always optional.
Block counts by size
The smallest portal needs ten obsidian, because the four corners do not have to be placed. A 5 by 5 frame needs sixteen, a 10 by 10 needs thirty-six, and a full 23 by 23 needs eighty-eight.
Why build a big one
For a player walking through, size makes no difference at all. It matters when you want to move things: minecart rails through a portal need the extra width, mob transport needs the height, and horses and boats simply will not fit through a minimum-sized frame comfortably.
Large portals are also a build feature. A 12-block archway with a purple shimmer inside is a genuine centrepiece, and the cost is just obsidian.
Lighting it
One flint and steel on any inside face lights the whole frame regardless of size. A fire charge or a lava source adjacent to the frame works too. If it refuses to light, the frame has a gap or one of the sides is a block short.
Getting the pair aligned
Size does not change how linking works. Coordinates still divide by eight on the way in and multiply by eight on the way out, and if you do not build the far side yourself, the game will drop a portal wherever it likes. Work out the exact matching position with the nether portal calculator and build the partner there, and the pair will behave predictably every time.