Rifty

I think the easiest way is to use a plugin.

A nice simple plugin to do as you describe can be found at https://www.ads-software.com/extend/plugins/social-media-widget/, I’ve used it on a couple of sites in the past.

If you’ve never installed a plugin before, download it and follow these steps;

1. Upload the social-media-widget folder and all contents to /wp-content/plugins
2. Activate the plugin through the ‘Plugins’ menu in WordPress
3. Go to Appearance->Widgets and activate the widget (Social Widget), set options and click save

If your theme is widgetised, you can just drag the Widget into ‘Footer’ on the Appearance->Widgets page.

Otherwise just Google how to Widgetize your footer.

Although it’s a pain I think the best way forward is to install WordPress again in the correct directory.

Here is a guide if you want to keep the /wordpress directory though;
https://codex.www.ads-software.com/Giving_WordPress_Its_Own_Directory