The easiest way is to build a portal nearby, travel to the normal world, fill your glass vials with water there and bring those back to the Nether.
You can fill as many vials as you can fit in your inventory and it won't take much time out of your brewing schedule.
You could also keep water in the Nether in a cauldron, but as that only holds 3 vials worth, it's slower than simply bringing the water to the Nether in vials.
gaming.stackexchange.com/users/3454/Joe Dovahkiin
In versions of Minecraft before the current 1.0.0 release, you could use the Silk Touch enchantment to get Ice blocks, and break them in the Nether to produce water source blocks.
However, this was patched, and they won't create water in the Nether anymore.
The only way to place water in the Nether, currently, is to place a Cauldron and fill it with water.
Sadly, it isn't as good as an infinite source, as it can only fill 3 Glass Bottles before needing to be refilled, but it's the only option for brewing in the Nether at the moment.
gaming.stackexchange.com/users/18/Kevin Yap
Create two ender chests, keep one and one world and the other in the nether fill it with buckets of water you can keep up to 27 buckets in an ender chest
it's the easiest way to get water in the nether.
gaming.stackexchange.com/users/122369/Nasty Hobbit
You really can't have a source of water legitimately in the nether, you can only put it from a bucket to a cauldron in vanilla.
You would need to use mods such as TooManyItems to spawn pure water that's not in a bucket.
It looks like vertically flowing water in the GUI.
This is the only way to get placeable water in the nether.
It won't sizzle, but be placed instead and flow.
One way to kind of keep the vanilla feel would be to make a bucket, find a water source, and "scoop up" the water by just giving yourself a water block and having the bucket empty.
gaming.stackexchange.com/users/16036/Jonny
Only raw water can be placed in the Nether.
If your single-player world has cheats enabled or you are an op on a multiplayer server, use /give <your name> <8 or 9> <amount> to get that.
8 is source water, whereas 9 is stationary water.
gaming.stackexchange.com/users/38781/Bo Garrett
Just exploring the nether, found my first nether fortress, and lots of netherwart.  Wanting to start brewing potions in the nether fortress, but getting a source of water is problematic.  Is there a way to get water into the nether in vanilla minecraft (i.e. no mods)?  I'd like an unlimited water source if possible.
Is there a way to get water into the nether?
gaming.stackexchange.com
<minecraft-java-edition>
gaming.stackexchange.com/questions/43782
gaming.stackexchange.com/users/16398/John
You can either place a cauldron and fill it with water, or travel to the normal world and fill your glass vials there. You could also use a mod like TooManyItems to spawn pure water. While carrying water in the Nether is a time consuming task, players detail plenty ways of doing so, including the use of modifications and commands.
The community describes what items can carry water into the nether. Usage of mods or admin commands is recommended.