How can I make a nether portal in minecraft without a diamond pickaxe?
A nether portal can be build by building a rectangular frame of obsidian. The minimum size for a nether portal is 4x5 blocks. After building the rectangle it needs to be activated by lighting it on fire using a flint and steel.

Without a diamond pickaxe you cannot mine obsidian so you must obtain it by other means such as finding it in chest. Obsidian can spawn as loot in villages, ruined portals, bastion remnants or nether fortresses. One popular method of building a nether portal without a diamond pickaxe is by using a lava bucket and a water bucket. Lava can turn into obsidian if water runs over it. With careful placement of lava and water, you can build yourself a nether portal without a diamond pickaxe or without any obsidian blocks.
nice thank you! which of the methods you mentioned is the fastest?
The speed at which the above mentioned methods of creating a nether portal varies. This is because in Minecraft, the generation of all features (including villages, ruined portals, etc.) are dependent upon the RNG (Random Number Generator) function of the game. This means that sometimes, it will be faster to find obsidian from loot chests, and sometimes it will be faster to find sources of lava, water, and iron (required to craft a bucket, which is used to move the lava and water).

Within the word record speedrun for random seed glitchless any%, a nether portal is constructed via the water and lava bucket method, as this is considered the fastest method on average.