Ten. A working nether portal needs ten obsidian blocks, because the four corners of the frame are decorative and the game does not check them.
The maths
The minimum frame is four blocks wide by five tall. That outline is fourteen blocks in total, minus the four corners, which leaves ten. Build the full fourteen if you have the spare obsidian and prefer how it looks — it works identically either way.
Bigger portals
Portals can be built up to 23 blocks wide and 23 tall. A larger portal is purely cosmetic for a player walking through, but it matters for anything you want to push through it: minecart systems and mob transport both need the extra space.
Every extra block of width or height adds two blocks of frame. A 5×5 frame needs 16 obsidian, a 10×10 needs 36, and a full 23×23 needs 88.
Mining it
Obsidian only breaks with a diamond or netherite pickaxe, and each block takes around ten seconds — less with Efficiency. Anything weaker destroys the block entirely and you get nothing.
The easiest source is a surface lava pool with a water bucket. Pour water across the top and the lava source blocks convert to obsidian where the two meet. Bring at least twenty blocks back: ten for the portal, four for an enchanting table, and spares for the return portal you will want to build at the correct coordinates.
Build the far side yourself
Do not let the game place your Nether portal for you. Coordinates divide by eight when you cross, so the matching spot may be hundreds of blocks from where the game decides to drop you, and two Overworld portals can end up sharing one Nether exit. Work out the exact position with the nether portal calculator and build the pair yourself — ten more obsidian for a link that behaves predictably every time.