<script src="https://code.jquery.com/jquery-3.2.1.js"></script>
<script>

$(document).ready(function(){
$(".add").click(function(){
var name = $("#name").val();
var surname = $("#surname").val();
var age = $("#age").val();
$.ajax({
url:"some.php",
type:"POST",
data:{name:name,surname:surname,age:age},
success : function(r){
$(".table tr:last-child").after('<tr><td>'+name+'</td><td>'+surname+'</td><td>'+age+'</td></tr>');
alert("Data eklendi.");
}
})

});
});
</script>

<style>
td{
border:1px solid #e1e1e1;
}

.add{
background:#222;
color:#fff;
padding:10px;
display:block;
width:100px;
text-align:center;
text-decoration:none;
}
table{
margin-bottom:20px;
}
</style>

<table class="table">
<th>My Example Table</th>
<tr>
<td>Name</td>
<td>Surname</td>
<td>Age</td>
</tr>
<tr>
<td>Emre</td>
<td>Çelik</td>
<td>20</td>
</tr>
<tr>
<td>Enes</td>
<td>Çelik</td>
<td>20</td>
</tr>
</table>
<form action="javascript:;" method="POST">
<label>Name</label>
<input type="text" name="name" id="name">
<label>Surname</label>
<input type="text" name="surname" id="surname">
<label>Age</label>
<input type="text" name="age" id="age">
</form>
<a  href="javascript:;" class="add">Add Data</a>