Overview
Abyss to Core
From the beginning of patch 0.4, the Abyss mechanic will now function like other core league mechanics such as Breach or Ritual - you'll be able to encounter randomly generated Abyss content in maps on the Atlas, where the map will have an Abyss icon if that content will appear in the map.

Abyss spawning randomly on a Map
However, just like any other core league, you'll also be able to target farm Abyss for its exclusive rewards by utilising Abyss tablet to force Abyss content to spawn within a map.

An Abyss Precursor Tablet
Abyss Precursor Tablets can also be rolled to obtain modifiers that change the content applied to that map, such as improving your chances to find Desecrated currency.
Abyss in the Endgame
Like other core league mechanics in Path of Exile 2, Abyss will also gain its own Atlas Passive Tree in patch 0.4.

The Abyss tree in 0.4
You'll be able to obtain points for the Abyss Atlas tree via interacting with specific Abyss content such as completing a basic Abyss encounter in a map, or completing an Abyssal Depths. The latter points will be obtainable by defeating specific Abyss bosses.
The points can be invested to empower the Abyss mechanics in your maps. This can range from simply adding more Abyssal monsters, making the content harder and more rewarding, to increasing the chance that you encounter Abyss bosses.

The Sprawling Rupture Notable
One node even provides a small chance to cause a nearby map to be overrun by Abysses upon completing an Abyss encounter.
Abyss Crafting
Notably, Abyss Desecration crafting is also going core, though access will be more limited than in patch 0.3 due to Abyss no longer showing up in every area. This will naturally result is Desecration currency bones being more expensive in trade leagues. However, Desecration crafting alongside Essences and Perfect currency Orbs will make up the basic tools to create strong progression gear in Path of Exile 2's patch 0.4, especially following the removal of the Homogenising Omen of Exaltation.
Desecrating Maps is also going away in patch 0.4 - you'll no longer need to spend so much time throwing countless Maps into the Well of Souls. Instead, some of the power obtained from the Desecrated Map modifiers is being moved to Precursor Tablets.