Nearly all the time, the Spanish m is pronounced basically the same as the "m" sound of English.
The main exception is that when a word ends in m and there are very few of them, frequently words of foreign origin the m is given the "n" sound. Examples of such words include álbum and mémorandum.
Sample words spoken by native speakers in the accompanying audio lesson on pronouncing the m are "lo siento mucho," "¿cómo está usted?" and "muy bien, gracias."