Well if you want to host the website yourself you need to install Wamp, or you can just buy hosting and a domain. You can use WordPress, or similar or you can learn HTML, CSS, PHP and javascript and MySQL. I recommend checking the web for this, look at youtube videos. One channel I like for tutorials is PHPAcademy on youtube. Good luck making your website!
They probably use a normal website hoster, where you just upload your website. But if you're thinking of the website design you can always look in the button, it will always stand who designed it, and if they used any template, it will stand what template etc. Hope this helps!