1. Make sure your application/config/ directory is writable by a web server. (Note, this is the application/config/ directory in the root of the archive).
2. Make sure application/files/ and its subdirectories are writable by the web server (or the world.)
3. Create a new MySQL database and a MySQL user account with the following privileges on that database: INSERT, SELECT, UPDATE, DELETE, CREATE, DROP, ALTER
4. Visit your Concrete website in your web browser. You should see an installation screen where you can step through the process of entering your database details, your administrative username details and more.
5. Upon completing this process, Concrete should be installed.
concretecms.com offers hosting and will pre-install Concrete for you:
Concrete CMS Hosting
http://www.concretecms.com/hosting/
Concrete CMS can also be installed with one click on other web hosts by using Softaculous or SimpleScripts. Check with your web host to see if you have these services enabled.