The needle: it all starts with a good needle.

This is a different needle than used with punch needle or embroidery, you do NOT put thread through a needle, but you press with a sharp point, loose thread by loose thread, into a (preferably woolen, but I work on velvet) surface, in the desired location. Because this needle has special hooks that you cannot see but can feel, and the wool (including the surface) has scales (like your hair), these scales will be rubbed into and against each other by the hooks of the needle. causing them to 'tangle': this is the felting process. The more often you pierce that spot with the needle, the better and firmer it will felt and therefore stay stuck.

Which wool: you work with wool or other natural threads that have the property of scales, just like your hair.
The wool has been processed for you (although it is also nice to clean, color and card your wool yourself, but this is a lot of work and requires some technique), and there are various types.
My wool comes from Italy, from DHG
Merino wool is the most common wool fiber available and popular for felting. It comes in almost every color imaginable and normally originates from Australia or South Africa. Merino wool is available in carded form and in sliver (wick) form.

CARDED: the wool is like a piece of cotton wool, all the threads are, as it were, intertwined, and you can use it to create beautiful structures and achieve effects in your work of art. (This is also perfect for 3D figures)
WICK:  (also called 'roving', 'tops' or 'sliver'): all threads/fibers lie in one direction and are connected together as a 'wick', this allows you to work with longer and finer threads, making your work of art less 'roughly structured'. Wick is very nice to use for fine details. (Like eyes etc). But feel free to try a combination of both!
Both wicking wool and carded wool come in various types, not only Merino, but also Maori, English wool, Scottish wool, Corridale, Bergschaf, etc. They also come in various thicknesses, expressed in 'microns'.
Another important thing: check carefully whether the wool is 'mulsing free'. The sheep is then treated in an animal-friendly way for the wool.
I only work with mulsing-free wool, natural coloring and not chemically cleaned.
And also try the Alpaca!
The possibilities are endless...

You also use a pricking mat, wool felt (on which your work of art is made) and enough bandages for your fingers (be careful: the needle is sharp!)