How can one develop cancer of the brain and the syptoms?

Several ways. There are tumors that originate in the brain itself, then there are metastatic tumors that originate elsewhere and spread to the brain. Symptoms vary widely, and can include headache, seizures, and sensory or motor disturbances. The specific genetic factors that lead to brain tumors are not well known, but family history, age, race and exposure to ionizing radiation & chemicals increase the risk.