You can find recipes for wands in various ways. Use a wardrobe to create wand outfits, then use the wand to transform your current clothes into those outfits.
Find Wand Recipes
There are recipes for different types of magic wands. There is a chance of finding them by popping balloons. You can also get a wand recipe from Celeste if she is on your island.
Put a Wardrobe in your House
To use wands, you will need to have a wardrobe in your house. If you don't have one, you can get a wooden wardrobe recipe by learning DIY from Tom Nook, then attending his customization workshop.
Create Wand Outfits
After you have a wand in your pockets or storage, and a wardrobe in your house, you can create wand outfits. Use the wardrobe and select Edit Wand Outfits, then choose a spot where you want to save the outfit.
When creating an outfit, keep in mind that the clothing items themselves will be put into the wand, so you won't be able to see them in your storage.
Also, if you want two different wand outfits to use the same clothing item, for example, two wand outfits that both use the same shirt, you will need to buy two of that shirt. Each outfit uses separate clothing items.
Wear Wand Outfits
Hold the wand and use it, then select one of your saved outfits. The clothing that you are currently wearing will be transformed to look like the wand outfit. If you want to remove the transformation, use the wand and select the current wand outfit. Your clothing items will go back to their original state.