Hagoromo Ōtsutsuki, the Sage of the Six Paths and one of the progenitors of what we know as chakra, developed a teaching which was meant to bring people together by sharing chakra. Known as Ninshū, his teachings were meant as a guide for people to share chakra with each other, living in harmony and peace. However as time went on and he too soon faded from the world, humanity all too easily discarded his teachings and instead created what we know today as Ninjutsu. By combining one's own spiritual and physical energies, humanity was able to create techniques that would otherwise be impossible to do. However, not all was lost for even where there is darkness, so too light shall be to illuminate the way.
Ninjutsu is a broad term for a variety of "ninja techniques" that help shape how you fight. They allow you to perform tasks that would otherwise be impossible or very difficult to do otherwise. Training in ninjutsu begins at the fundamental knowledge of what chakra is and how it can be applied to almost everything and everyone. I'll forgo the explanation as we both understand very well what it is. Once one has grasped the fundamentals, the user then applies his chakra to a medium such as himself, another person, or other objects. The most common usage for chakra is in creating elemental techniques. It is comprised of two stages, Nature Transformation and Shape Manipulation. Nature Transformation is quite simple as what you are doing is just transforming your chakra to mimic certain properties of an element of the basic five (earth, air, fire, water, or lightning). Some elements are more versatile than others but all depend on the user's knowledge and experience. Shape Manipulation is rather simple at first because you are changing the shape of the chakra you are creating but what is quite challenging is controlling your chakra and applying nature transformation as well. Why? Because of the degree of chakra control that is required to combine those two aspects together to form a new technique/element.
Anyways, our focus isn't on elemental chakra but it does deal with it. This subject of Ninjutsu we are studying refers mostly to applying chakra to mediums such as weapons though I believe there are some that don't require chakra. As far as I am aware, Ninjutsu is can be broken in to many categories but I believe it is generally best to break them into two categories: Ninjutsu and Ninpō (Ninja Techniques and Ninja Art).
Ninjutsu refers to a specific technique that is used in fighting and to some extent, isn't very flexible. Ninpō on the other hand, refers to the art of fighting and is usually more flexible because it allows you to use your imagination and creativity. In other words, Ninjutsu refers to the act itself and Ninpō refers to the style of fighting (like a CFS). This is evident when you compare say throwing a kunai in battle normally versus Tenten who employs many different ways to utilize kunai in her battles, thus creating her own style of fighting and being a more effective fighter in her own right. The same goes for Sai. Most of his techniques, though not covered in this lesson, employ the usage of ink and how he uses it in battle to create his own style.