Since ownCloud supports WebDAV protocol to access your files, you need a client to connect to your ownCloud server. Make sure you enable WebDAV in apache config file. ownCloud has its client to connect however I would like to show you how to do this by using my popular open source file transfer program WinSCP.
You need to just select WebDAV, write the hostname, user name and password as shown. Do not forget to add a forward slash
/ to the end of ownCloud WebDAV URL.
If you enable SSL on your domain, you can select SSL/TLS encryption, which is a secure and preferred way. WinSCP might ask your password again after you press login. After that you are in.