Most of the time, the Spanish c has the "k" or "hard c" sound of English, although perhaps a bit softer or less explosive. The sound of the "c" in "scatter" or the "k" in "breaks" is basically the same as the "hard c" of Spanish.
In nearly all of Latin America, the c also has the "s" sound when it comes before an e or an i. This is much like the situation in English, where what is basically the same sound is heard in words such as "faces" and "fanciful."
When c comes before other vowels, such as a or o, it retains the "k" sound.
In most of Spain, the c before an e or an i is pronounced much like the "th" in "thin" or "think." Contrary to common belief, this is not a lisp, but is simply the way the letter is pronounced.
The Spanish z has the same sound as does the c before an e or i. So in most of Latin America it has an "s" sound, and in most of Spain it has the unvoiced "th" sound.
Except in words of foreign origin (such as zigzaguear, to zigzag), the z does not appear before before an e or an i; it is replaced by a c instead. Thus the plural of lápiz (pencil) is lápices, and the plural of faz (face) is faces. Note that the change in spelling does not reflect a change in pronunciation.
Note that in Spanish the ch, which used to be considered a separate letter, has its own sound.
To hear these sounds, listen to our brief audio lesson on c and z. Words and phrases spoken by native speakers in this audio lesson are color (color), con permiso (with permission, excuse me), cigarro (cigar), zapato (shoe) and cereza (cherry).