To get started, you need an Alchemy table (8 planks, 8 nails, 1 glass flask, 1 hammer). Then you will need a lot of fairy dust, which can be obtained by finding the Magic Flower and turning it into dust.
Potions
Berry head - Reduces the heads of your characters. (10 raspberries, 1 magic dust)
Resistance to cold - Makes your character resistant to cold. (10 bear berries, 1 magic dust)
Craftsman's potion - Reduces crafting time from 1 minute to 1 second. This potion can be crafted in three different ways. (5 grains / buckwheat / quinoa, 1 magic dust)
Glow Potion - Light up the area around your character. (1 glowing mushroom, 1 magic dust)
Health potion - Heal your character for 3 hearts. (5 Echinacea, 1 Fairy Dust)
Heat resistance - Makes your character resistant to heat. (5 Desert Sage, 1 Fairy Dust)
Life change - Temporary change of your body / gender. (1 toadstool, 1 magic dust)
Melon head - Doubles the size of your character's head. This potion can be crafted in two ways. (10 Desert Sage / Wild Melons, 1 Fairy Dust)
Flight - Your character will temporarily be able to fly. (5 snapdragons, 1 fairy dust)
Speed - Increases the speed of your character for a while. (5 bones, 1 magic dust)
Force - Raises the level of your character and increases the speed of breaking blocks. (5 spinach leaves, 1 magic dust)
Breathing underwater - Your character can swim underwater without losing air. (1 coral, 1 fairy dust)