How to get Newsletter form shown in footer block?

I'm not 100% sure what you mean by 'get', I thought you meant add it but as it's already there in the blank and Luma theme and the previous answer is pretty much correct I presume you want to move it so I'll base my answer on that.

Quick answer:

<move element="form.subscribe" destination="*DESTINATION-HERE*" />

The explanation:

Find the block name

First you need to find the name of the block you want to move, to do this I searched all of Magento's module and theme XML files for 'newsletter', to do this I used the following search term vendor/magento/**/frontend/**/*.xml. With enough experience you'll know off the top of your heard that it's subscribe.phtml so it does get easier with time. This returned quite a few files, the one that is responsible for adding the footer newsletter block is vendor/magento/module-newsletter/view/frontend/layout/default.xml. This is the code that renders the block:

<referenceContainer name="footer">
    <block class="Magento\Newsletter\Block\Subscribe" name="form.subscribe" as="subscribe" before="-" template="subscribe.phtml"/>
</referenceContainer>

Move the block

Now we know the block name, we can move it. To do this we use this code:

<move element="*BLOCK-NAME-TO-MOVE*" destination="*DESTING-BLOCK-OR-CONTAINER-NAME*" />

So inside app/design/frontend/*PACKAGE-NAME*/*THEME-NAME*/Magento_Theme/layout/default.xml we can move the block, like so:

<?xml version="1.0" ?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
    <body>
        <move element="form.subscribe" destination="content" />
    </body>
</page>

In the above example the newsletter signup form will be moved to the content, you can swap content with any block or container you wish to place it in.

Screenshot

enter image description here

If you did want to add it to a new theme:

If you did actually mean add it then paste the below code into app/design/frontend/STORE-NAME/THEME-NAME/Magento_Theme/layout/default.xml

<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
    <body>

        <referenceContainer name="footer">
            <block class="Magento\Newsletter\Block\Subscribe" name="form.subscribe" as="subscribe" before="-" template="subscribe.phtml"/>
        </referenceContainer>

    </body>
</page>

if you are creating your own them in

view/frontend/layout/default.xml

put tag like this

<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
    <body>
<referenceContainer name="footer">
            <block class="Magento\Newsletter\Block\Subscribe" name="form.subscribe" as="subscribe" before="-" template="subscribe.phtml"/>
        </referenceContainer>
    </body>
</page>

don't forget to clear your layout cache

hope this will work for you