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n Wordpress, there are two main parts to the website's front and backend: the core WP files and the theme that is used. (And other important aspect to a WP site is the database, where all content is stored, including text/images entered in the admin backend.)
Core WP files are not to be changed because they get overwritten with each update. What you want to work with is the theme. Look in Appearance>>Themes and see what the active theme is for the site. It will also tell you the name of the folder the theme files are in.
With FTP, go to root/wp-content/themes/your-theme-name. That's the php, html and css source of the displayed part of the site. Uploaded images are in /uploads/, and plugins in /plugins/.
See http://codex.wordpress.org/Theme_Development to get an idea of how themes are built and how to modify them.
See the rest of the docs at WP to see how to work with plugins, add other javascript correctly so it doesn't conflict with WP's included javascripts, etc. All the docs you really need are at wordpress.org