If you do not have a computer that can do this then the router must support it directly. There are a number that do but the vast majority don't. If you have a soft copy of the manual you can search for dyndns. If you do not find it is a good sign it is not supported.
You have 2 options, replace the router from one off the supported list or get a old junk machine to use behind the router.
I have some webcams wirelessly on a Westell 327 router. I have been viewing them from a remote location. Lately the ip address is changing a lot and I can no longer find them. The only things on the system are the webcams and the router - not a computer. Have been told to try a dyndns account and have the router send the account the current ip. Have set up the account but I cannot figure out how to have the router send the updated ip info. The cameras are port forwarded. Please be basic - not an expert here. Using Windows XP on a Verizon DSL line. Thanks in advance for the help.