Load the Elytra tutorial.
First we need a splash potion. The hardest ingredient to get is a regular old Spider Eye from a spider. You'll need to be playing on a difficulty other than peaceful for this.
Enemy spawn tip
Head to an area where you can see a decent amount of space. Slightly outside the village to the left (west on the map) is another little hut village with a hill behind it. This place works great. Save the game here at night on peaceful. If you aren't on peaceful, save it, reload it on peaceful, then save it. Now just reload this save on easy to get a new monster spawn. You should have line of sight to a bunch of areas. You can walk around for 30 seconds or so and if you don't see a spider reload.
With your spider eye, head back in to the village and head East/right of the beacon to find the brewing area. The area slightly to the right of the brewing area has a fireworks chest. Open it and grab
Now head to the chest next to the brewing stand and grab:
- Empty Bottle
- Nether Wart
- Blaze Powder
Use an empty bottle on the sink to fill it with water.
Now use the brewing station.
- Place the Blaze Powder in the upper left
- Put the Bottle of Water in the leftmost potion slot
- Put the Nether Wart in the top slot
- Wait for the Awkward Potion to brew
- Put the Spider Eye in the top slot
- Wait for the Potion of Poison to brew
- Put the Gunpowder in the top slot
- Wait for the Splash Potion of Poison to Brew
Head back to where you found the spider and use the tip above to get the Witch to spawn. I only had to load three times before I could see one. Save before you throw the potion just in case it doesn't pop.