There are a LOT of web hosting companies out there and it is a big industry. To get started with your site, you’ll need to select and sign up for an account with a web host.
I recommend you sign up with Hostgator. You can get a web hosting account with them for about $9/month and it has all the capability you’ll need. In fact, this very website is hosted on Hostgator. They have great support and they’ll treat you right. I’ve been in this business for 13 years now, so I know Hostgator is one of the good ones.
As your site gets much busier, you might need to move to a more powerful server (Hostgator can do that, too, or you can decide to move your site somewhere else). But, for people just getting started, go with Hostgator.