<meta charset="utf-8">
<form>
    <div>
        <label for="ime">Ime: </label>
        <input id="ime" type="text">
    </div>
    <div>
        <label for="prezime">Prezime: </label>
        <input id="prezime" type="text">
    </div>
    <div>
        <input id="submit" type="submit" value="Pošalji">
    </div>
</form>
<p></p>

<script>
    var form = document.querySelector('form');
    var ime = document.getElementById('ime');
    var prezime = document.getElementById('prezime');
    var submit = document.getElementById('submit');
    var para = document.querySelector('p');

    form.onsubmit = function (e) {
        if (ime.value === '' || prezime.value === '') {
            e.preventDefault();
            para.textContent = 'Morate upisati i ime i prezime!';
        }
    }
</script>