belief is important, spells work as the result of the energy, not the belief. to cast a spell you charge energy, focus on the task, and visualize your intended outcome. once the spell is cast, you should continue working towards your goal as if you never cast [so you don't sit back and go 'why go to work early? i cast a spell for more money']
Scott Cunningham in his book Wicca: A Guide for the Solitary Practitioner defines there are three types of energy personal power, earth power, and divine power. personal power is the energy your body needs to survive, earth power is the energy found in herbs, crystals and other things found in nature. divine power is the energy we use in spell casting. relying on earth power isn't enough, and using your personal power will weaken you and could potentially make you sick. to cast spells properly you need to learn how to tap into the divine power of the universe.
finally, just because you believe, doesn't mean all spells work. the divine energy is natural, and is ruled by the rules of nature. therefore it cannot contradict nature. you are human. any spell to change that will not work no matter how much you believe.