[Mikael86]

Удалённо подключите библиотеку Jquery
<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script>

<input type="text" id="add_persona_inp">
<button id="add_persona_btn">add</button>
<p id="add_persona_p"></p>

family = [];
$('#add_persona_btn').click(function(){
     text = $('#add_persona_inp').val();     
     family.push(text);
     summ_person = family.length;     
     $('#add_persona_p').html(summ_person);
})