Everything would be so easy. Just Upload the files, make sure that your wp-config File is still in the root directory. And your page is up ans running. Well, except if you are using Filezilla 22.214.171.124 because this version has problems with uploading the entire File Trees. It uploads first and second level folders but nothing below and this causes strange behaviors when you access your WordPress page.
It is really a pitty, that I thought that wordpress is the reason for the problem. But who would ever expect such a bug in Filezilla. Nevertheless it seems that the problem has been solved in the latest nightly of Filezilla. (They show the ticket as fixed in their bug tracking system).