To find the Deep Dark biome in Minecraft, it is located deep underground in the Overworld, typically below zero altitude (Y level 0). It is most frequently found beneath mountainous regions or plateaus. You can search for it by exploring deep cave systems, especially those under mountain biomes. The presence of sculk blocks (dark turquoise with light spots) is a good indicator you are near or inside the Deep Dark. The biome can also contain Ancient Cities, which are structures found typically at around Y -52 or lower, close to bedrock. If searching manually is too slow or difficult, Minecraft offers a command you can use in chat (opened with T):

/locatebiome minecraft:deep_dark

This command will give the coordinates of the nearest Deep Dark biome, and you can teleport or navigate to it directly. It's advisable to be prepared with good equipment such as night vision potions and good armor when exploring the Deep Dark due to its darkness and the presence of the Warden mob which can spawn if triggered by certain blocks like the sculk shrieker.