<div class="total-price">Общая сумма: <span class="value">350</span> руб.</div>
<script>
var priceNode = document.querySelector('.total-price .value').firstChild;
var priceValue = parseInt(priceNode.nodeValue, 10);
alert(priceValue);
</script>

<div id="total_price" style="text-align:right;">Общая сумма:
  <b>350</b>руб.</div>
<script>
  alert(+total_price.innerHTML.replace(/\D/g, ''));
</script>

<div id="total_price" style="text-align:right;">Общая сумма:
  <b>350</b>руб.</div>
<script>
  alert(+document.querySelector('#total_price b').innerHTML);
</script>