Many cable companies are phasing out DOCSIS 1.1 modems anyway.
To find out what kind of a modem you have, visit the modem manufacturer's website. This information should be on the bottom or back of the modem.
I'll be honest: Cable modems aren't glamorous technology.
In fact, you probably haven't thought about yours since it was installed.
If possible, scan the file for malware before performing the firmware upgrade.
Newer routers will likely make it very easy to download and install the firmware directly from within the router administrative console.