Run command below to install nginx.
sudo apt-get install nginx
By default, Nginx automatically starts when it is installed. You can access the default Nginx landing page to confirm that the software is running properly by visiting your server's domain name or public IP address in your web browser.
but if you need latest version, you may need to add official ppa.
sudo add-apt-repository ppa:nginx/stable
sudo apt-get update
sudo apt-get install nginx