Before you can spawn the Warden, you must first find the Deep Dark biome. This is the only area of the map that the Warden will spawn in, and even then you'll have to complete certain tasks to summon it.
The Deep Dark biome can be a bit difficult to find, but your best bet is to find a channel of caves and continue to follow it down until you locate the biome. You'll know you've reached the new area when you find a lot of sculk blocks, which are dark and speckled with blue luminescent dots.
Once you reach the Deep Dark, you'll have to locate the sculk shriekers. This block emits a "shriek" when activated by stepping on it or triggering a nearby sculk sensor, temporarily deteriorating the player's vision for a few seconds.
You'll have to trigger these sensors four separate times to get a Warden to spawn; this number is specific to the player, meaning you can trigger four different sensors or the same sensor four times and a Warden will still appear.
The Warden will come up through the ground and continuously emit the darkness effect, obscuring the player's vision as it roams. While the Warden is blind, it can detect players based both on smell and vibrations from sound. The more vibrations it detects, the more agitated and, therefore, more aggressive it becomes.
Unfortunately, it only drops a single sculk catalyst and five experience when killed, so it's not necessarily worth it to spawn this mob often.