Hey, @reniar1
First you must make a new component
php artisan make:livewire register
if you want to make a component in subdirectory you must name your folder following the component name with a dot (.)
php artisan make:livewire auth.register
After that set up the route
Route::get('/register', Auth\Register::class)->name('register');
Then update your livewire/auth/register.blade.php
and call the route in your application.
I highly recommended seeing Redering Components Section
In the docs
Or you can take a look at this thread:
https://laracasts.com/discuss/channels/general-discussion/is-blade-component-basically-livewire