How can I use a multimeter to check the signal-to-noise ratio output of my soundcard?

You can't measure the SNR with a multimeter - sorry. You need a pretty expensive and sophisticated audio test set:

http://ap.com/products/p1-ats1

Around $8000

Here is a great article on audio test equipment:

http://www.proaudioreview.com/article/190

To measure Signal-to-Noise-Ratio (SNR) you need to perform two measurements: 1) The Signal and 2) the remaining noise after the signal is removed.

Your multimeter may be sensitive enough to measure the Signal (volts range), but may not be able to measure the Noise (milli-volts range).

Also, your multimeter should be capable of having an AC Bandwidth to include ALL of the frequencies within the audible spectrum.

If you can do that, then take the two measurements, then use the formula: dB=20*log(Signal/Noise).

Example: Signal=2 volts; Noise=2 milli-volts; Ratio=2/.002=1000; log(1000)=3; 20*3=60 dB.

Note; To be correct, you are actually measuring Signal+Noise to Noise ratio, but for high SNR the result is practically the same. Let's take the case of Signal= 2 volts and Noise= 0.2 volts. The actual measured ratio would be (2+0.2)/0.2 = 11 not 10.

In the case you mentioned: 100 dB SNR, referred to 2 volts Signal, the Noise is .00002 volts (20 micro-volts). dB=20*log(2/0.00002) =20*log(100000)=20*5 =100 dB. So, like Daniel K said, you need a pretty good meter for that.