You just need this in the htaccess file in your old domain's document root:
Redirect 301 / http://www.mynewsite.com/
If both your old site and new site share the same document root, then you need mod_rewrite instead:
RewriteEngine On
RewriteCond %{HTTP_HOST} ^(www\.)?myoldsite\.com$ [NC]
RewriteRule ^(.*)$ http://www.mynewsite.com/$1 [L,R=301]