If you are trying to get smooth basalt, the main method for getting is via amethyst geodes. The reason why is that the geodes will have an outter layer of smooth basalt.
So if you want to find a amethyst geode, you can find athemspawning after Y=70 underground and around bedrock levels. You can also find the geodes spawning occasionally on the overworld, exposed both in beaches and underwater.
You can also make smooth basalt from regular basalt, which you can get in the nether Soul Sand Valley biome. In this biome, basalt will spawn naturally as pillars. The next location you can find basalt is in the Basalt Delta biome, as the entirety of the biome is made up of the block for the most part.
Once you find basalt, you can then mine it with any type of pickaxe, and when you do, you can create smooth basalt by putting it inside a furnace and cooking it.
Along with this, the player can also make polished basalt if they place the regular basalt inside a stone cutter. If you don't have a stonecutter already, you can make one with three stone blocks and one iron ingot.