Welcome to SMF.
1. Download the Full Installer Package
and save it to your computer.
2a. You can either extract the files to your computer now and upload them to your webhost or....
2b. Upload that full install zip file to your webhost and then in their control panel choose to extract the file contents.
3. Once that's done, you need to go into your database section and create a new database for the forum. Then create a new username and password in the database. Assign this new username to the database and give it full privileges. Make sure you remember the information entered here.
4. Go to your browser and now point it to http://www.yoursite.com/install.php
(replace yoursite.com with your actual site and correct the path to the install.php if that's not where you installed it). Enter your forum and database information (you just did this earlier) and you should be on your way to using SMF shortly.
You should also look at the SMF Online Manual
as it should have steps on how to do this as well and other common questions that may come up.