This is pretty straight forward:
    var previous = document.createElement("input");
    previous.type = "button";
    previous.value = "<-";
    previous.className = "leftBtn";
    previous.onclick = function(){
        console.log("CLICK");
    };
It won't display click in console. If I try to put it directly in the input header with chrome dev tools, it outputs texts so I know the button works. I just have no idea why it doesn't work when I assign the function with javascript.
EDIT:
function createCalandar(id, year, month){
    var date = new Date(year, month, 0);
    var daysInMonth = date.getDate();
    console.log(id+" "+year+" "+month);
    
    var size = Math.sqrt(daysInMonth);
    
    var currentDay = 1;
    var header = document.createElement("div");
    header.className = "staticHeader";
    var previous = document.createElement("input");
    previous.type = "button";
    previous.value = "<-";
    previous.className = "leftBtn";
    previous.onclick = function(){
        console.log("CLICK");
     
    };
    
    var next = document.createElement("input");
    next.type = "button";
    next.value = "->";
    next.className = "rightBtn";
    
    header.appendChild(previous);
    header.appendChild(next);
    
    var table = document.createElement("table");
    table.className = "calandar";
    for(var x=0; x < size; x++){
        var row = document.createElement("tr");
        for(var y=0; y < size; y++){
            var col = document.createElement("td");
            row.appendChild(col);
            if(currentDay <= daysInMonth){
                col.innerHTML = currentDay;
                col.onclick = function(e){
                    console.log(currentDay);
                }
            }
            
            currentDay++;
        }
        table.appendChild(row)
    }
    
    var htmlLocation = document.getElementById(id);
    htmlLocation.innerHTML = header.outerHTML+"<br />"+table.outerHTML;
   
}
function createCalandarNow(id){
    var date = new Date();
    createCalandar(id, date.getYear(), date.getMonth());
}
function nextCalandar(){
    
}
function lastCalandar(){
    
}
createCalandarNow("calandar");html,body{
    margin:0;
    padding:0;
}
#calandar{
    position:absolute;
    right:10;
    bottom:20;
    width:200;
    height:200;
}
#calandar input{
    width:50%;
    cursor:pointer;
}
#calandar .leftBtn{
    position:absolute;
    
    left:0;
}
#calandar .rightBtn{
    position: absolute;
    right:0;
    
}
.calandar{
  
    border:1px solid gray;
    width:100%;
    height:100%;
    text-align: center;
}
.calandar td{
    border:1px solid white;
   
    
}
.calandar td:hover{
     background-color:lightgray;
    cursor:pointer;
}
.calandar .staticHeader{
    position:static;
}<title>Scheduler</title>
<div id="content">
    <div id="calandar">
    
    </div>
</div> 
    