Free hosting is good because it's free! You actually don't have to pay to get on the internet at all anymore (well, once you have a computer and modem). There are places that will provide you with a free connection, free email, and free web hosting. The drawbacks to free hosting are possible unreliability of their servers (your pages being slow to get to, or inacessible), having to deal with their software, and (usually) having ads on your pages. However, it's free, and if you're just starting out or testing the waters, it's a great way to go.
Paid hosting is good because you get an internet connection, email access, web space, and more options. You can get fairly cheap hosting this way ($12/month if you shop around), it's more reliable, and you don't have to deal with funky software. You can use whatever email program you want (as opposed to free web-based email), you'll have more options for doing fancy stuff with your site (cgi, .htaccess, domain names, etc.), and you'll (probably) have better customer support.
It's pretty easy to find an internet provider or web host. Maybe there's a local one that you know is pretty cheap, or you can ask your friends or just look it up in a search engine. Once you have web space, you're ready to start uploading.