To create a back-up of your application: ask the current developers for the source code, not just the application folder, but also css and javascript files and other assets like pictures and icons. Otherwise, you need the ftp credentials for access to the website files. Download all files to your computer. In that case, you also have a back-up of all additional files (documents, uploaded files etc.).
And very important: create a back-up of the database(s) your website depends on. If it's MySQL, you must log in to PhpMyAdmin and export the database to an SQL file. If anything goes wrong, you can restore the database.