I would suggest using a service like noip. You can create an account for free and get access to a static IP/sub-domain. They provide a linux (open source) client that you have to install on your machine that you want to reach from outside.

Or if you are behind a router you can just configure your router to work with noip and your router will always update noip with its current IP-address. Then all you have to do is configure port forwarding, that your router forwards outside packets to the desired machine and port.

It's really a great service and easy to use. Good luck!