With local Ubuntu boxes, whether they're connected directly or using a switch, you can use hostname.local to connect. So, if your laptop is called bambuntulaptop, then you can connect to it using bambuntulaptop.local.

For non-local connections, you'll have to use an IP address or setup a dns server. You can use ddclient coupled with a service like dyndns.org.

NAT isn't really relevant with regards to ssh. You'll need to forward port 22 to the right machine, or configure your ssh server to use another port and forward that one. Port 22 is the default ssh port.

You must not allow non-protected accounts. There are thousands, or hundreds of thousands of computers who are scanning for things to abuse. Allowing any user on the internet to run programs on your computer is a seriously bad idea. Ubuntu is secure, but not that secure. In fact, I don't think you will be allowed to use non-password protected accounts with ssh. If you wanted to do that, then you'd need to setup keys. That would be another question.

The command to establish the connection itself, could hardly be any easier: ssh username@host. In other words, reusing the example from above; ssh [email protected].