Update packages

sudo apt-get update

Install nginx

sudo apt-get install -y nginx

Enable and start nginx

sudo systemctl enable nginx && systemctl start nginx

Install PHP8.1 and PHP8.1-FPM + some important modules

sudo apt-get install php8.1-cli php8.1-fpm php8.1-curl php8.1-gd php8.1-mysql php8.1-mbstring zip unzip

Enable and start php8.1-fpm

sudo systemctl enable php8.1-fpm && systemctl start php8.1-fpm

Configure PHP-FPM to use UNIX socket

vim /etc/php/8.1/fpm/php-fpm.conf

When viewing the /etc/php/8.1/fpm/pool.d/www.conf file you will see that the PHP8.1-fpm is listening to the socket at 'listen = /run/php/php8.1-fpm.sock'

Activate php-fpm in nginx

Below server_name directive

vim /etc/nginx/sites-enabled/default

location ~ \.php$ {
       include snippets/fastcgi-php.conf;

       # With php-fpm (or other unix sockets):
       fastcgi_pass unix:/run/php/php8.1-fpm.sock;
}

Restart both nginx and php7.2-fpm

sudo service nginx reload

sudo systemctl restart php8.1-fpm