Yea you should be able to do it fairly easily. Like JKam said you'll need a domain and a host.
Once you have those two - you can either use their one click install OR manually set it up yourself. It will definitely be easier if you use their one click installs unless you know what you're doing.
Manual setup usually includes
1. Set up FileZilla or any FTP client
2. Set up a database (can do within your host's cpanel)
3. Download latest wordpress install from
WordPress ? Blog Tool, Publishing Platform, and CMS
4. Upload unzipped files to your public_html folder for your host
5. Run wp-install and entering the database information
Feel free to PM me if you need any help