If you can do tunisian crochet flat, you already know everything you need to do it in the round. You just need slightly different equipment: a double ended hook and two strands of yarn.
All about double ended hooks
There are two types of double ended hooks. One is a a single piece of wood or metal with a hook on each end. The second is two hooks connected with a cable (often this is two interchangeable hooks). Both versions need to have the same sized hook on both sides and both versions can be used for any pattern.
Double Ended Hook Double Ended Hook with Cable
I personally prefer using the two hooks with cable for larger projects like sweaters and the single piece hook for smaller projects like hats but I do swap based on what I actually have.
Yarn for "Tunisian in the round"
Two strands of yarn are needed. One for the forward pass and one for the return pass. It is easier to have two seperate balls/cakes but sometimes you only need one (like for smaller projects like hats) and then I use both ends on a center pull cake.
How to do tunisian crochet in the round
Tunisian in the round is one of the few times you need to turn your work in tunisian crochet.
First, work your forward pass as normal. When you get to the end of the row (or there are too many stitches on the hook to comfortably continue), turn the fabric so the wrong side is facing you.
Next, using the other end of the double ended hook and the second strand of yarn, yarn over and pull through 2 loops. Repeat the yarn over and pull through two loops until there are 3-4 loops on the hook. This motion is just like a regular return pass but with the wrong side of the fabric facing you.
Finally, turn the fabric so the right side is facing you and continue the forward pass. Whenever the number of stitches on your hook gets uncomfortable or you reach the end of a round, turn and work the return pass until 3-4 loops are left on the hook.