You can use a webserver such as Apache to serve HTML files. Apache can be installed by using the commands below depending on your OS.

Ubuntu:

sudo apt-get update
sudo apt-get install apache2

CentOS:

sudo yum install httpd
sudo service httpd start

I installed a wordpress website before but everything is configured by Digital Ocean; what am I supposed to do for normal html site?

After you have installed apache like MDS says with that command, you can upload your HTML site inside

/var/www/html

If you want to configurate apache to handle domains, you need to create a VHOST. You can learn more about this in another tutorial