There are free and paid web hosting packages available on the internet and I strongly suggest you to use paid web hosting packages because of their high quality and fast speed.
SMF forums can only be built and published on web hosting packages which support php scripting language and MySql database (Linux system). Today, almost all web hosting packages support php and mysql but if you have to choose, I suggest you to select Linux system.
Where to Get Web Hosting Package
You can buy paid web hosting from Hostgator. I have used it for 3 years and still using their baby hosting plan. Click here to get a shared web hosting package from Hostgator.
You can also get free web hosting package from awardspace.com. There are lots of web hosting companies which offer free web hosting packages but awardspace.com offers one of the best free web hosting package on the internet.
Create Database
After you get a web hosting package, you should log in to control panel of your web hosting package and create a database. In some hosting packages you may need to create a database username and authorize it. Briefly, you have to create a database and a database username that have permission to use database.