There are several issues to address in order to successfully connect two different Macs in this scenario.
Consider signing up for a dynamic DNS provider such as FreeDNS so that you can use a domain name rather than an IP to initiate a connection from the local Mac to the remote Mac. With a small amount of scripting, or by creating a launchdaemon or launchagent, you can have both ends update their IP automatically.
Next, you'll need to make sure that any router, firewall or other edge device on both networks have the proper ports open. Apple's kbase article specifies ports 3283 and 5900, but make sure you have considered the risks of opening these commonly-used ports to the public Internet.
Also you will need to forward those ports from your router (which has the public/internet IP address) to your home Mac (which has a private IP address not available on the Internet). You may have to contact your ISP if you are unsure how to do that as there are as many ways of doing this as their are different types of routers.
Depending on the network hardware on both ends, you might also be able to leverage a solution such OpenVPN or IPSec to create a persistent tunnel, but that won't remove the need to update the configuration when either end's dynamic IP changes.
Finally, enable Remote Desktop access on both Macs. Open System Preferences > Sharing and enable Remote Management. Then, open the Apple Remote Desktop application on both Macs, choose Preferences (command-,), and from the Security pane, enable "Allow control of this computer when this application is running."
Exposing these machines to the public Internet entails risks. Make sure you are using long, strong passwords for the local accounts, that are not used anywhere else - longer is better than 'complicated'. Have known-good backups and test them regularly. Finally, make sure that enabling remote access to any device on your office's network won't violate your organization's security policies, AUP, etc.
ARD is still a good app for remotely managing and controlling Macs, but you may also be better served with a dedicated remote access tool such as LogMeIn or TeamViewer.