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.