A commonly used ink in the Middle Ages was iron gall ink; there is an article about it on Wikipedia. The problem is that it uses some ingredients that are not readily available everywhere. For example, here where I live in South Africa, I have no idea where to get hold of oak galls, or iron sulfate for that matter.
So here is recipe that works reasonably well, using some commonly available materials. You will need vinegar, steel wool and tea, plus some suitable containers in which to mix them.
First, take some steel wool, put it into a container and cover it in vinegar. Leave it to react for a week:
Some of the steel wool dissolves in the vinegar, forming iron acetate (I think; my chemistry is as rusty as the gunk that forms in the glass). You will notice that quite a lot of bubbles will form on the surface of the steel wool as the reaction runs, and a rusty mess begins to float on top and sticks to the sides of the glass, which is why it is best to use an old one that you do not want to drink from again. However, lower down the solution is quite clear, and it is this bit that we'll use.
I now brewed up a very strong tea. I used two tea bags for half a mug of water and let it steep for quite a while to get it as strong as possible.One can use such a strong tea as an ink substitute as well, but it tends to be rather on the light side. Based on what I read the early pioneers in South Africa used the leaves of the protea tree instead of tea, and I have a feeling eucalyptus leaves will work as well, or any other leaf that contains a lot of tannins, but I have not tested this personally. I mix the tea with some of the clear steel wool/vinegar solution in a more or less 50:50 mixture:
One has to experiment with different mixtures, because the colour of the ink depends on that, but also on how strong the tea was, and the precise consistency of the steel wool/vinegar mixture, so no two batches ever look precisely alike.
Mostly, one gets a brownish ink, though I have on occasion managed to produce a fairly dark, bluish-black ink as well. One can use various instruments with which to write:
The ink is initially quite light in colour, but it darkens a bit as it dries, rendering the writing quite legible. Note though that as with real medieval ink, it is not archival: the acidity tends to eat into the writing surface, and will in time damage or entirely destroy it.