Moving a Contao installation from a local server to a live server is not much different from installing a fresh Contao version, except that you are using the files from your local installation instead of the Contao download archive and an SQL dump of your local database.
Open your FTP program, connect to the target server and upload all files from your local Contao installation.
The easiest way to create a MySQL dump is to use the database administration
tool "phpMyAdmin". If you are a server administrator, you can also use the
mysqldump utility of course. Log into "phpMyAdmin", choose the database that
you want to export and click the "Export" tab in the top menu. It is important
to adjust the export settings according to the screenshot below to minimize
MySQL version compatibility problems.
Open "phpMyAdmin" on the target server and create a new database for Contao. Depending on the server configuration, you probably have to use the server administration panel (e.g. "Plesk" or "cPanel") to create new databases. Select the empty database and click the "Import" tab in the top menu. Then upload the SQL dump of your local database and start the import.
Finally open the Contao install tool of the new installation (the password should be the same as for your local installation) and adjust the database configuration if necessary. Then go to the back end and log in with your username and password.