<script language="JavaScript">
  function addInput()
  {
    var oblast = document.getElementById('inputy');
    var nwInput = document.createElement('input');
    var nwLine = document.createElement('br');
    
    nwInput.type = 'text';
    nwInput.name = 'vstup[]';

    oblast.appendChild(nwInput);
    oblast.appendChild(nwLine);
  }
</script>

<form>
  <div id="inputy">
    <input type="text" name="vstup[]"><br>
  </div>
    <input type="button" name="add" value="Přidat" onClick="addInput();">
</form>