You don’t need any origami tools to fold paper. All you need is your hands, a piece of paper, and a flat surface to fold on. Easy. You can do it at home, you can do it at work (oops, did I really say that?). You can do it on the train, you can do it on the bus. You can do it in a coffee shop, you can do it in a restaurant (see dollar-bill origami and napkin folding).
That being said, your paper folding experience can be more fun and easier with some select tools. Here are some things that you may want to consider.
Origami Paper : there are numerous types of origami paper to choose from. They range in price, size, and quality too. Read all about it here.
Paper Cutters: a paper cutter is essential for those who do not buy pre-cut square sheets. There's basically two types: guillotine and razor. Click to read more.
Origami Paper Storage: once you have a good collection of origami paper, you will neeed a way to store and organize the paper. Click here to get some ideas for paper storage.
How to Display Origami: your origami models are special and deserve to be treated so. See the different ways you can show off your models.
Folding Bones: Don't know what it is? It's sometimes called a bone folder. Still don't know? Click and learn.
Origami Books: Free, onlline, origami diagrams are great but sometimes it's just nice to have it bound, organized, orderly, collection - another words a book.
You may be interested in reading about how people design origami and the different ways you can teach origami. For example, is it better to have written instructions, photographs, diagrams, or videos?