How to pass some parameters to function called in addEventListener? [duplicate]

You don't. Use anonymous functions:

document.getElementById('date_right').addEventListener('click', function () {
    switch_date(1);
}, false);
document.getElementById('date_left').addEventListener('click', function () {
    switch_date(-1);
}, false);

Or use named functions which do not take arguments:

function onRightDateClick() {
    switch_date(1);
}

function onLeftDateClick() {
    switch_date(-1);
}

document.getElementById('date_right').addEventListener('click', onRightDateClick, false);
document.getElementById('date_left').addEventListener('click', onLeftDateClick, false);