They need to register through the Marketplace merchant portal. Requirements are Name, Vendor Name, Email address (preferably a designated business email) and PayPal email. You cannot edit these fields later, be thorough.
Well then, how do they register?
Some people run private marketplaces and provide the merchant portal URL via email or some other form of private communication. If you want to open it up to the public, you have to create a link to your merchant portal in your store. Whether you hard code it into your theme, or just add it as a navigation link through Shopify.
Here's some code that you could use to add a link to a theme:
<a href="http://yourURL.marketplaceadmin.com" target="_blank" class="merchant portal">Merchant Portal</a>