You are treated as a Missouri resident for admission and tuition at public two-year and four-year colleges and universities if you were honorably discharged recently, moved to Missouri, and declared your intent to become a Missouri resident. At a community college you also have to live in the taxing district of the college you attend.
Tell the admissions or registrar office at the Missouri public institution you are applying to that you are claiming veteran residency for tuition purposes, and give them your discharge paperwork.
Your DD214 showing a recent honorable discharge, and documentation that you have moved to Missouri and intend to become a resident.