You have to attend college. Everything varies from state to state.
EDIT:
This is what i found for the Kansas City, Missouri Police Dept.
Im assuming it would be somewhat the same for another city in Missouri.
Law Enforcement Qualification Requirements
United States citizen
21 years of age upon completion of academy training
High school diploma or GED equivalent
Valid driver's license from any state and obtain a Missouri driver's license by the date of appointment
Live in City of Kansas City, Missouri within twelve (12) months of employment
Pass the Police Officer entrance examination, which measures an individual's ability in arithmetic, reading comprehension, grammar and writing. A minimum score of 70% in each category is required
Pass the physical agility test
Proportional height and weight according to department standards
A minimum of 20/200 vision uncorrected, correctable to 20/20 with normal color vision
Ability to communicate clearly and concisely using clear verbal and good writing skills
Physically capable of operating a department issued handgun and shotgun
Pass a polygraph examination
Pass a background investigation
Pass a psychological evaluation
Pass a physical examination
Must meet other requirements as specified by the Kansas City Missouri Police Department during the pre-employment process
Disqualifiers
Dishonesty
Past pattern of drug abuse and/or use of certain controlled substances
Excessive traffic conviction history
Excessive city ordinance, misdemeanor violation convictions or outstanding warrants
Felony convictions or misdemeanor convictions directly resulting from felony charges
Dishonorable discharge from the United States Armed Services