Depends a bit on what you want to do.
Is the problem scaling or disaster recovery?
* If you just want to scale up the application and add more performance / a bit more redundancy on just the application server you are going to need a new application server and some way to load balance between different application servers (round robin dns, loadbalancer, geodns, logic in your app, etc.)
See https://www.digitalocean.com/community/articles/how-to-set-up-nginx-load-balancing or https://www.digitalocean.com/community/articles/how-to-use-haproxy-to-set-up-http-load-balancing-on-an-ubuntu-vps
You probably won't gain much by putting the new application server in another data center (if the database server or the network connection goes down between your app server and database server, your site is down anyway).
* If you have scaled up the application servers and need to scale up the database (mysql or postgresql) you are looking at clustering, replication, log shipping, and other heavy stuff (if you need this you probably already have 4-5 application servers already)
See https://www.digitalocean.com/community/articles/how-to-set-up-master-slave-replication-in-mysql or https://www.digitalocean.com/community/articles/how-to-set-up-master-slave-replication-on-postgresql-on-an-ubuntu-12-04-vps
If you are using some of the nosql databases(cassandra, mongodb, etc) this can be reasonably simple to do by "just" adding new servers.
If you do some of these scale ups correctly you are also going to add a bit of redundancy, if you have 3 applicationserver and a decent loadbalancer one of the application servers can crash and none of the users will notice.
* If you want to add disaster recovery to your system you are basically going to add both app servers and database servers in another data center. You will have to deal with all the above issues (with at least 2-3 times the complexity) and also think about how to deal with different split-brain scenarios (what happens if the only thing going down is the network between the data centers, what to do if the same data is changed differently in both data centers at the same time, etc)
This article covers how to set up a simple load balancer on a DigitalOcean droplet with nginx. The tutorial covers setting up a round robin loadbalancer that can then direct site visitors to one of a set of IPs