javascript: get a function's variable's value within another function

nameContent only exists within the first() function, as you defined it within the first() function.

To make its scope broader, define it outside of the functions:

var nameContent;

function first(){
    nameContent=document.getElementById('full_name').value;
}

function second() {
    first();
    y=nameContent; alert(y);
}
second();

A slightly better approach would be to return the value, as global variables get messy very quickly:

function getFullName() {
  return document.getElementById('full_name').value;
}

function doStuff() {
  var name = getFullName();

  alert(name);
}

doStuff();

Your nameContent scope is only inside first function. You'll never get it's value that way.

var nameContent; // now it's global!
function first(){
    nameContent = document.getElementById('full_name').value;
}

function second() {
    first(); 
    y=nameContent; 
    alert(y);
}
second();