The American National Standards Institute Classroom Acoustic Standard recommends noise levels not exceed 35 dBA in an empty classroom. The primary concern is noise coming from within the school (HVAC and other noises) and noise from outside the school (transportation noise). The level for transportation noise is 40 dBA under some circumstances, but there is no scientific reason why 40 dBA of transportation noise is any less problematic to learning than 40 dBA of other noises. The standard does not cover classroom appliances, but they should not raise the empty classroom noise levels above 35 dBA for the students (particularly those closest to the appliance).
Accurately measuring classroom background noise levels requires hiring an acoustical consultant or at the very least using a calibrated Type II sound level meter. Acoustical experts often charge $150-200 per hour. Type II meters and calibrators can be purchased for about $800.
There are inexpensive sound level meters that give good estimates of the background levels. These are more than good enough to start identifying problem areas, for use by students investigating classroom noise, or as an analytical tool before hiring an acoustical consultant. The best low cost option is to purchase an Extech 407727 Digital Sound Level Meter.
The Extech meter, while the best option, is still not perfect. It is somewhat limited because it only goes down to 40 dBA and cannot calculate an hourly average. Using it will identify major problems, but miss many boarder line cases where the noise level is between 35-40 dBA. The Extech meter costs $79. You can learn more about it at: http://www.extechproducts.com/products/extech/407727.html
The other popular low cost sound level meter, the RadioShack meter, is cheaper, but it only goes down to 50 dBA, which is low enough to identify only very significant problems.
Set the meter you get to "A" weighting and "Slow" response. Test the locations where students sit in a classroom with the HVAC system running in an empty classroom. Although the standard doesn't include appliances, they too should be running and not raise the level above 35 dBA.
Since the meter you are using probably only goes down to 40 decibels, you should not get any readings. If you do, try to identify the source by listening for what sounds loudest and turning off the interior sources one at a time (for example, first the appliances, then the HVAC). The source of the noise may also be outside.
The standard uses a one-hour average noise level (something more expensive meters calculate), so occasional small spikes in noise level may not exceed the standard. It is very likely, however, if you get readings using your 40 dBA level on the meter, that you are have found a noise that exceeds the standard.