So far I have this code that has been automatically generated by Wordpress to define the permalink structure:

# BEGIN WordPress
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteRule . /index.php [L]
</IfModule>

# END WordPress

Does anyone know how I should update it to forward my old domain to my new domain?

Basically I have:

newdomain.com and olddomain.com

Both pointing to the same location, if I visit olddomain.com then it shows in the address bar, however if I then click any link on the site, the address changes to newdomain.com

But how would I set it so that anyone who visits olddomain.com will be automatically forwarded to newdomain.com?

Thanks

Try this

RewriteCond %{HTTP_HOST} ^(www\.)?OLD\.com$ [NC]
RewriteRule .* http://www.NEW.com%{REQUEST_URI} [R=301,L]

You'll need to change OLD and NEW to your domains of course.

I use:

redirect 301 /url_old.html http://www.dominio-new.com/url-nova/

Thanks, would either of these work if I simply added it after my existing .htaccess code? Or should I replace part of it?

put your redirect first in the .htaccess

Great thanks, all sorted now