The letter C has no sound of its own; it represents either a k-sound or an s-sound and sometimes even a ch-sound /tʃ/. I have seen student worksheets for the alphabet with /s/, /k/ and /c/. The first two notations represent the s-sound and the k-sound respectively. However the letter C has no sound of its own and the notation /c/ is meaningless nonsense.
Originally there was no letter C. In ancient history, a people called the Etruscans changed the letter G into a C to fit their language. Eventually the Romans copied them and later the letter C got passed on into English. In the Roman language, Latin, the letter C was only used to represent /k/, in Latin, Caesar was pronounced like Kaiser and so forth. In the old British language, Welsh, there is no K and C is used only for /k/. In Old English, and Latin, the letter C was also only used to represent /k/. However after the 1066 invasion of England, English words borrowed from French or Latin often used a letter C for /s/. Some older English words got respelled according to this new pattern. Words that used to be spelled with a C for /k/ got respelled with the letter K. For example: king in Old English was cyning, take was tacan and break was brecan.1
Most words where the letter C makes a /s/ are from (Norman) French. For example2: celery (céleri), circle (cercle), cider (cidre) and city (cité). Some English words spelt with an S for /s/ were sometimes respelled with C for /s/ to match the spelling pattern for French words. Examples3 include, twice (twies), ice (is) and mice (mys). In these words the letter after the C was most often the vowels I or E.
Words in which a soft C is followed by the letter Y are often borrowed from Latin. For example4: cycle (cyclus), cyst (cystis) and cylinder (cylindrus). There are many words ending in -cy. They use the abstract noun-suffix of quality / to have the property of, from the Latin suffix -cia. For example: To have a chaplaincy is to have the job of a chaplain (or the place where a chaplain works). To have a bankruptcy is to not be able to pay one's debts. To have literacy is to be able to read and write.
The letter C is usually pronounced /s/ when in front of the vowels I, E or Y in words of French or Latin origin. Words like soccer5 are not of such an ancient origin. I will cover the SC combination next week. C can also be pronounced with a ch-sound, a sh-sound or even be silent; these situations will be covered the following week. Double-C will be covered in the week after that.