I currently have two webservers behind a load balancer that are running my websites. I'm considering buying an SSL certificate for one of my websites and converting it to https. What mechanics to I need to considerer as far as IP addresses and load balancing go?
You can use nginx as a load balancer and configurate it to correctly handle the server certificates just as normally would happen.
All the configurations are explained in http://www.cyberciti.biz/faq/howto-linux-unix-setup-nginx-ssl-proxy/ Instead of using the self-signed certificates, a purchased one can be used.
I have this working two different ways for two different sites now.
Install the certificate on each of the servers behind the load balancer. The load balancer accepts requests on port 443 and forwards them to the web servers unmodified. The responsibility for the encryption rests at the web server level.
Install the certificate on the load balancer itself. It accepts requests on port 443, handles the encryption and then makes unencrypted requests to the web servers on port 80.
As others have stated, it depends on the capabilities of your load balancer. When the load balancer can handle the encryption, it is very convenient to let it do so.