[ruslan_mart]

<button class="color" id="red" name="button" value="red" onclick='change_color(this.value)'>red</button>
<button class="color" id="orange" name="button" value="orange" onclick='change_color(this.value)'>orange</button>

function change_color(color) {
    if(color) {
         document.body.style.backgroundColor = color;
         window.localStorage.setItem('bgColor', color);
    }
}

window.addEventListener('DOMContentLoaded', change_color.bind(null, window.localStorage.getItem('bgColor')));