Magento 2 – How to Make Changes (Edit Core Block) in a Block

First of all, we need to add Constructor injection method to our custom select class: (Edit: we don't need to add Constructor Injection, we need to add the sequence module)

    <?php
    namespace Mike\Newselect\Block\Product\View\Options\Type;

    class Select extends \Magento\Catalog\Block\Product\View\Options\Type\Select
    {
        public function __construct(
            \Magento\Framework\View\Element\Template\Context $context,
            \Magento\Framework\Pricing\Helper\Data $pricingHelper,
            \Magento\Catalog\Helper\Data $catalogData,
            array $data = []
        )
        {
            parent::__construct($context, $pricingHelper, $catalogData, $data);
        }
        .....

We need to add the :

<?xml version="1.0"?>
<config xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:Module/etc/module.xsd">
        <module name="Mike_Newselect" setup_version="1.0.0">
            <sequence>
                <module name="Magento_Catalog"/>
            </sequence>
        </module>
</config>

http://devdocs.magento.com/guides/v2.1/extension-dev-guide/build/module-load-order.html

Second, copy vendor/magento/module-catalog/view/frontend/templates/product/view/options/type/select.phtml to our custom module app/code/Mike/Newselect/view/frontend/templates/product/view/options/type/select.phtml

You will have to create your custom module in "app/code/[VendorName]/[ModuleName]"

Here you will have to overwrite the block you would like to change using magento2's di.xml.

Now for example you we can create a module "app/code/Foo/Bar".

Firstly you need a registration file which will register the new module. We need to create a file app/code/Foo/Bar/registration.php, in which we add:

<?php
\Magento\Framework\Component\ComponentRegistrar::register(
    \Magento\Framework\Component\ComponentRegistrar::MODULE,
    'Foo_Bar',
    __DIR__
); 

Inside here you can create a di.xml at "app/code/Foo/Bar/etc/di.xml". In the di.xml we need to add a <preference/> node to overwrite any core classes.

<preference for="Magento\Catalog\Block\Product\View\Options\Type\Select" type="Foo\Bar\Block\Product\View\Options\Type\Select"/>

So in my case the module will overwrite the class Magento\Catalog\Block\Product\View\Options\Type\Select and instead the custom class will be loaded Foo\Bar\Block\Product\View\Options\Type\Select

Now we need to create a file at "app/code/Foo/Bar/Block/Product/View/Options/Type/Select.php" and our new class should extend the core class.

<?php

namespace Foo\Bar\Block\Product\View\Options\Type;

class Select extends \Magento\Catalog\Block\Product\View\Options\Type\Select
{

    //method you would like to overwrite

}

Also you will have to run the following command to activate the new module:

php bin/magento setup:upgrade

If your thinking of file based overwriting as it was done in Magento 1, it is no longer possible in Magento 2