Consonants are divided into identifiable categories according to three main sets of criteria. They can be classified by the articulator used to stop the airflow, by the way the interruption of air occurs, or by the voicing of the consonant. Each of these three methods of classification can be useful to know if you have any problems with articulation. If you practice saying and singing each of these sets of consonants, you can familiarize yourself with sounds and avoid some of the common problems for singers.
A standard guide for studying pronunciation is The Singer's Manual of English Diction, by Madeleine Marshall. This book offers a complete guide to clear enunciation of each letter and sound. It also lists rules for how to connect words smoothly and distinctly. This is an important reference book for any singer. Another great resource is Diction for Singers by Joan Wall.
Look at this list of articulators and the sounds they produce. Practice saying each letter while feeling the place in your mouth or throat that identifies the point where the air is stopped.
Certain pairs of consonants are formed in the same way and use the same articulators, but one is voiced, or has vibration, and the other is not voiced. An unvoiced consonant can't make any sound by itself but will be heard as soon as its neighboring vowel is voiced.
Say the consonants in the following list and notice that you can't isolate the unvoiced half of the list. If you can say it, it's because there's a vowel following the sound. But you should be able to feel the humming vibration of the voiced consonants.