I'm not sure when I began mixing non-traditional "inks" to use for calligraphy. It's probably when I stumbled on Bleedproof White and it definitely needs to be mixed before it can even be used.
First, pick a non-traditional "ink" that you'd like to mix.
I've used watercolors, gouache and even $1 craft acrylic paint to mix for calligraphy use. The sky is the limit and I encourage you to experiment.
Then you'll need water, an ink container, and something to stir it all with. Simple as that.
I've heard of other calligraphers using gum arabic, but I ended up using what I had on hand - tap water and a toothpick. For the water, I often take it straight out of the faucet, letting it slowly drip or I use an empty ink bottle with it's dropper.
Consistency is absolute key. The goal is to create a milk-like ink consistency.
The ink must have a consistency like that of milk. The true test is if it flows smoothly out of your nib. If it blobs up in the nib and doesn't come out, it's too thick and need more water. If it's too runny, there's too much water. Add and mix in a little bit of your "ink" back in.
It's trial and error, but when you get the hang of it, you can have all sorts of inks available at your fingertips.