How can I make my computer accessible anywhere (via SSH preferably). I have Ubuntu installed on it.
Is there a way to set up dyndns.com using dynamic IP without any router changes?
If you have a router, then you will need to forward port 22 to your computer for SSH to function (unless you're running it on a different port, in which case you'll need to use that port instead, but the default is 22)
Dynamic DNS clients can run on your computer, though some router firmwares have support for it depending on your host (DynDNS is rather popular). DynDNS offers a number of clients for windows, mac, and linux.
Simply running the DynDNS app (99.9% chance they provide it) on your computer will synchronize your external IP with DynDNS's records. After that, simply SSH to the URL you register[ed] with DynDNS.