To allow unregistered users to request to become vendors you have to activate the Enable Vendors registration in “My Account” page option you can find in YIT Plugins -> Multi Vendor -> Frontpage.
The option, in Multi Vendor -> Frontpage lets you activate the registration of the vendors directly from the “My Account” page of the shop.
In order to make the option work correctly, the registration in “My Account” page should be already enabled from WooCommerce > Settings > Account
The user, after registration, can have access to his/her own reserved area (url site/wp-admin) by inserting the username (acquired from the pair “Owner First Name” and “Owner Last Name”) and password.