How: Previously I used the ssh found in crosh (ALT+SHIFT+T > ssh ...) but the crosh ssh freezes if you lose your connection. The crosh will freeze for ~5 minutes before you can close your now worthless terminal tab. This happens a lot if you are on 3G and makes ssh impossible to use. My wireless cuts out enough to make this too frustrating to use.
Now I use secure shell from Google (https://chrome.google.com/webstore/search/secure%20shell). This app is fantastic. It is very fast and you can kill it whenever you please.
I have a rented linode which I ssh into and hack away in vim. Best development experience I have had.
I mostly use my chromebook at home not mobile. My experience is that since I am happy in the terminal I don't need a full powered PC for development. The chromebook is perfect for snatching an hour here and an hour there for development, since I have a day job and a family. My 17" quad-core laptop gets very little use these days.
I love the keyboard on my chromebook, although I miss the 'end' key almost every day.
Problems: I only test my web-app regularly in chrome. So I tend to build up safari and firefox css bugs over time and have to fix them in lumps.