A Dried Ghast gradually changes into a Ghastling when it remains submerged in water.
In the OjiCra world, I brought a Dried Ghast home from a Nether Fossil and watched over it beside the castle town fountain until the Ghastling appeared.
This article separates the official Minecraft Java Edition 1.21.6 mechanics from the timing and behavior I observed in that session.
Where to Find a Dried Ghast and How to Craft One
The official Minecraft Java Edition 1.21.6 release notes explain that Dried Ghast blocks can be found in Nether Fossil structures.
In OjiCra, I found a Nether Fossil where several Bone Blocks stood out in the Nether landscape.

Looking closely between those Bone Blocks revealed a block with a sad face.

That was the Dried Ghast.
It can be mined and carried home as an item, but the official notes state that its hydration level is not preserved when the block is mined.

If you do not find one in a Nether Fossil, you can also craft one with 1 Soul Sand block and 8 Ghast Tears.
Keep It Submerged in Water for About 20 Minutes
According to the official notes, a continuously waterlogged Dried Ghast goes through three hydration-level changes over approximately 20 minutes before spawning a Ghastling.
In OjiCra, I placed the Dried Ghast in the castle town fountain.

At first, it kept its dry appearance while sitting below the surface.
As I continued watching, its face changed and green particles became visible around it.

After those changes progressed, the Dried Ghast block disappeared and a small Ghastling appeared above the water.

The official notes also say that the hydration level decreases on the same timescale when the block is no longer waterlogged, so it needs to remain submerged while it develops.
I Watched Nearby for 16 Minutes and 6 Seconds
The timing in this section is an observation from this OjiCra session, not the general official duration.
After placing the Dried Ghast in water, I moved far away for 9 minutes and 19 seconds. In this particular world and session, its visible hydration stage had not progressed when I returned.
Once I came back and stayed near the fountain, I watched for 16 minutes and 6 seconds before the Ghastling appeared.
The official guideline is approximately 20 minutes. My 16-minute-and-6-second record is only the amount of time I watched nearby during this attempt, not a duration that should be expected in every world.
This single observation also does not prove that moving far away always stops the process.
A Ghastling Can Be Tempted with Snowballs
The official release notes state that Ghastlings can be tempted and fed with Snowballs.
I also held a Snowball and walked away in OjiCra, and the Ghastling followed me.

Keeping Snowballs ready gives you a way to guide the newly born Ghastling.
Dried Ghast Growing Steps
For Minecraft Java Edition 1.21.6, the full sequence is:
- Find a Dried Ghast in a Nether Fossil, or craft one with 1 Soul Sand and 8 Ghast Tears
- Place the Dried Ghast so that it is waterlogged
- Keep it submerged for the official guideline of approximately 20 minutes
- Wait while it passes through three hydration-level changes and becomes a Ghastling
- Use Snowballs to tempt and guide the Ghastling
The story of finding the Dried Ghast in the Nether and watching it emerge in the fountain is in OjiCra Season 3 Episode 41 (Japanese).
The next story, where the Ghastling grows up and takes its first flight with a Harness, is in OjiCra Season 3 Episode 42.
You can find more hands-on notes in the Minecraft Memo archive.