Battery light came on and car is not charging.

Hello, 1999 Beetle TDI approx 100,000 miles. Today the battery light came on, so I checked it with a volt meeter, approx 12.14 volts at idle. It's not charging.

Should I first check/troubleshoot the voltage regulator? If so, how do I test it? Then how do I also check the alternator?

Thanks!