Knowing how spells work is kind of difficult. By its very nature, magick is impossible to define and to describe in any concrete terms. There is no simple way to explain how it works besides just stating clearly that it does work.
Part of it will depend on the kind of spell you do. Are you calling on a God or Goddess for assistance? In that case, your spell is a lot more like a prayer and you are hoping a Deity will give you some help.
We all contain energy within us, and we all have the ability to use the energy of the universe that surrounds us. The trick is to harness and direct that energy. By focusing your thoughts and actions during a spell, you can learn to do that. Visual imagery and rhyming words help you tap into the right-side of your brain that handles all creative thought.
In addition, you can further fine-tune your desires by adding all of the "extras" that go into a spell (stones, colors, herbs etc.) Each of these items has its own form of energy that you are bringing into the mix.
Over many centuries of magickal practice, it's generally known which elements work best for which purpose (malachite for financial abundance, or rose quartz for love. This is why I say you do not need extra supplies, just that they come in handy and add extra power to your work.
Does this explain how spells work? Well, probably not that well. At least you have a general idea of how magick can manifest itself. The most important fact is that it does work.