The main thing you need for Tunisian crochet is a long crochet hook, called an afghan hook or a Tunisian crochet hook. The length of your hook determines the width of the projects you can crochet -- well, that's not entirely true, because you can make panels and then seam them together. But your panels would be close to the same length as your hook.
The Right Crochet Hook
There are hooks available in a variety of different sizes and lengths.
I find it most comfortable to work with hooks measuring anywhere from 10" to 14" long. They also make longer, flexible hooks available, which I have but have not mastered yet. I found I didn't really enjoy working with the flexible hooks, although I may revisit it again at some point when I am feeling more up for the task than I was at the time I first tried.
If you like to crochet with worsted weight yarn, a size J is a good choice for most crocheters. Most crocheters find they need a slightly larger hook for Tunisian crochet than they do for traditional crochet. It can be challenging to work Tunisian crochet with bulkier yarns -- for one thing, because the fabric gets to be really thick, and for another, because it is a challenge to find large-sized Tunisian crochet hooks (or at least, that was true last time I was in the USA -- about a year and a half ago. Time has passed, and that may or may not be the case now.)
At that time, I found Tunisian crochet hooks available for sale at both Joann and Hobby Lobby. Hopefully you should be able to find one locally, but there are plenty of online retailers who sell them if you prefer mail order.
Other Tips and Supplies
Other than the hook, it's mostly the same tools you'd use for traditional crochet -- scissors, tapestry needle, tape measure / ruler, etc.
I do often combine Tunisian crochet with traditional crochet, so if you want to make some of my patterns you would need both types of hooks.
If you want to do cables, a knitter's cable needle might also come in handy, depending on how the cable is constructed. I would say, in that case, find a pattern that appeals to you and refer to the materials list for guidance in whether you'd need one, or not.
Here are some more helpful links for your Tunisian Crochet needs.