You can set the port Vine uses in the preferences. Be aware that it has a persistent server mode and a manual mode. It defaults to 5900, but you van easily change that to 5901 or whatever you like. The VNC server built into the OS uses 5900, so I use 5901 for Vine.
You just need to open a port on your router to point to the IP of the Mac. You will want to give the Mac a static IP. If you have trouble opening the port provide us with the model of router you have.
Also since Vine (or any flavor of VNC) is not secure I'd suggest opening a port to SSH on your Mac and tunnel your Vine connection over SSH. You can use a command like this to connect, although change the 5900s to the port you use. If you open the port to SSH you don't need to open the port for Vine.
ssh -L 5900:127.0.0.1:5900 username@public_IP
After running that command on the the VNC client computer you can then VNC to localhost and your session will be secure. You could accomplish this in safari by typing vnc://localhost
Also, instead of using your public IP you could instead get a DynDNS.com account so when your ISP gives you a new IP you'll still be able to connect. Your router may support DynDNS updates automatically, or you can get their app to keep up to date.
You would then use:
ssh -L 5900:127.0.0.1:5900 username@your_account.dyndns.org