Drupal - How do I simply make the whole site use a secure connection?

If you want to redirect all of your pages to be forced to use SSL then add this to your .htaccess file.

# Redirect to HTTPS
RewriteCond %{HTTPS} off
RewriteCond %{HTTP:X-Forwarded-Proto} !https
RewriteRule ^(.*)$ https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]

This should be placed directly after RewriteEngine on if you have no previous rewrites.

Start by reading Enabling HTTP Secure (HTTPS). Please ask more specific questions and/or update your question if that doesn't help.