I have been wrestling with this for a few months now. Here is how far I got. You will need to keep both servers updated with all of the same files so it does not break. That means that any plugin or file you upload to one server, you do to the other. Keeping them both in sync is a must.
As for the database, that is the way I have it set up now. I have one main database one server 1, and I have it set so that server 2 gets its database from server 1. This ensures that all of the comments and posts are the same whent your site is visited by different people on different servers.
The basic solution is to set up your main server wp-config with all of the info you set up, then for server 2 you would need to put the login information for server one, but where it says "local" you would put the ip address of the server 1 where the database is being brought in from.
I really had a pain in the @ss setting this up. I strongly suggest talking to your hosting provider and getting them to help you set this up as they also had to make some apache changes so that they are the same on both of my servers so they handle info the same way. It was a HUGE pain getting it all figured out. One issue I have that might be permanant is that I cannot use WP-SuperCache plugin as it messes up some info on my servers. Dunno why exactly but I just cant use it. Other than that I think I have it all set up.