Making Mossy and Overgrown Variants of Underground Stone
What the variants are
Each stone family has two weathered looks. The mossy form is Andesite Mossy Cobblestone, Basalt Mossy Cobblestone, or Black Granite Mossy Cobblestone. The overgrown form is Andesite Overgrown Stone, Basalt Overgrown Stone, or Black Granite Overgrown Stone. These are separate blocks from the plain stone and cobblestone, so you cannot get them by mining ordinary Andesite, Basalt, or Black Granite.
Finding them underground
Both variants generate naturally in their home regions. When you are tunneling through an Andesite area, keep an eye out for patches of Andesite Mossy Cobblestone and Andesite Overgrown Stone mixed into the walls. The same applies to Basalt Mossy Cobblestone and Basalt Overgrown Stone in Basalt regions, and Black Granite Mossy Cobblestone and Black Granite Overgrown Stone in Black Granite regions. Mine them with a pickaxe and they drop themselves.
Building with them
Use the mossy and overgrown blocks as accents against the plain stone, cobblestone, and brick shapes. Because they share the same family, Andesite Mossy Cobblestone sits naturally next to Andesite Cobblestone Slab, Andesite Cobblestone Stairs, and Andesite Cobblestone Wall. The overgrown stone pairs well with Andesite Slab, Andesite Stairs, and Andesite Wall. Apply the same mixing logic to Basalt and Black Granite builds. If you want a ruined or aged look, scatter the mossy and overgrown blocks irregularly rather than in clean lines.