To get this achievement you need to make a 4 x 5 block vertically oriented portal to the other dimension, The Nether, by building it from obsidian and then igniting the bottom interior surface with a flint & steel.
Obsidian can be found deep underground where water flows onto lave pools, but I find the the easiest way to make obsidian is to find an existing lava pool (you can sometimes find them on, or close to, the surface), then take a bucket of water and pour it so that it flows over the lava surface. You can then mine the obsidian with a diamond pickaxe. Depending on where you poured it, the water will also flow into the gaps you make, making more obsidian if it comes into other lava deposits beneath. Note that the water has to be poured on pooled, not flowing lava.
You can omit the four corners of the portal, so it only requires 10 blocks of obsidian rather than 14.