After straightening out your HTML a bit by replacing your "smart" quotation marks with "normal" ones (as Sebastian Simon mentioned in his comment)
I simplified your code a bit and added a significant part: 
- return validate(...)in your- onclickpart makes sure that the return value from your validation function is used to determine whether to submit the form or not.
- return falseinside your function will cause the form not to be transmitted (if you return- truethe form will be submitted)- 
- 
- function validate(textid){
   console.log(document.querySelector('#'+textid).value);   //Works
   //more code to take actions depending on thisValue 
   
   return false;  // if you don't want to submit the form yet
}
 - <form name="demoForm" id="demoForm">
  <label id="givenNameLabel" class ="blueText">Please enter your given name:
  <input type="text" name = "givenName" id= "givenName" value ="nn">
  </label>
  <button onclick ='return validate("givenName")'>Validate this entry</button>
</form> 
 
 
 
Here is an alternative version. I suspect, that you can probably do without the ids of the individual elements and you can re-use your validation function for other input fields, if you address the input fields in a "relative" way, i.e. by looking for a previousElementSibling of the clicked button.
The Array.prototype.forEach.call() is a clumsy looking construct that applies the Array method forEach() to the nodelist returned by document.querySelectorAll()  (this version should even work in the Internet Explorer). Inside the forEach() function the click-event is bound to the validate(ev) function for each button with class "validate".
Array.prototype.forEach.call(document.querySelectorAll('.validate'),
  function(el){el.addEventListener('click',validate)});
function validate(ev){
  var el=ev.target.previousElementSibling;
  console.log('validating element '+el.name+', the value is: '+el.value);   
  //more code to take actions depending on el.name and el.value 
   ev.preventDefault(); // in case you DON'T want to submit the form yet ...
}
<form name="demoForm" id="demoForm">
  <label class ="blueText">Please enter your given name:
  <input type="text" name="givenName" value="Carsten">
  <button class="validate">Validate this entry</button></label><br>
  <label class ="blueText">Where do you live?
  <input type="text" name="myhome" value="Hanover">
  <button class="validate">Validate this entry</button></label><br>
  <label class ="blueText">What are your hobbies?
  <input type="text" name="myhobbies" value="coding">
  <button class="validate">Validate this entry</button></label>
</form>