How do I get a Droplet's dedicated IP address?

Droplets do not have dedicated IP addresses, only leased ones.

When creating a new Droplet, we lease it a static IP address from an available pool. This address remains associated with the Droplet until a user chooses to destroy their Droplet, in which case the address returns to the available pool.

However, in addition to the Droplet’s static IP, you can have one Reserved IP address and up to 16 IPv6 addresses, depending on which datacenter the Droplet resides in.

Reserved IPs do not support SMTP traffic.
Configure your firewall to allow outgoing traffic through ports 80 and 443.
What to do in a blackhole event when your traffic stops routing properly.