FTP login is more than enough to install wordpress. You just need to upload your wordpress’s root folder content (not root folder itself) via FTP and then open your site’s admin section via browser something like this http://www.yoursite.com/wp-admin/. Then you will see wordpress installation step. Follow that steps and your wordpress installation is done.
NOTE If you are uploading wordpress from local or from other domain (not fresh setup) then don’t forget to change database name, username, password, host in wp_config.php available in root folder of wordpress.
Following steps must be done only after you have a database ready to install wordpress because on installation you need to specify database name, username and password. And database can’t be created with FTP.