Ninjutsu are techniques used for combat that requires chakra to produce a certain effect. Chakra is the combination of the physical energy gained through old school training and spiritual energy gained through meditation and mental focus. When both energies combine you can use handseals to combine the two in order to use ninjutsu techniques. The handseals are there to mold the chakra and command it to do a certain thing. Chakra is physical and spiritual energies combined but spiritual energy is basically your soul which is another way of saying your concentration. You could say chakra is Vegito while spiritual energy is only Goku.
Love the DBZ example at the end, well done ^^
Something i need to mention though, handseals limit the chakra used for a certain technique, it doesn't helps you mold chakra for it, but advanced users showed that they can use some techniques without handseals, what happens is that you mold chakra for a certain technique, use handseals to specify and limit the exact amount of chakra you will be using, then release the technique.
Also, chakra can be used in different basic methods, like igniting dormant explosive tags, allowing you to "stick" on a normal surface or liquid substance, like walking on a tree or walking on water, it can also be used to enhance your punches and kicks and gives it extra impact power.
Anyway, what i want you to start doing is, release chakra out of your legs in a constant pattern, steadily and slowly, and start walking up that tree. *points to a tree nearby*