ca ? k
co ? k
cu ? k
ci ? s
ce ? s
cy ? s
c at the end of a word ? k
c before L or R or T ? kl or kr or kt (ex. clap, cross, connect)
ch at the beginning of a word and followed by a vowel ? usually as in chalk, children (? in Russian)
ch in the middle of a word (ex. echo, archaic) ? usually k
ch at the end of a word ? almost always as in chalk, children (? in Russian)
ch followed by an r ? kr
tch ? very similar to chalk, children. look up examples and listen. If you pronounce it the same as chalk or children you will be approximately correct.
ck ? k (c is essentially silent)
C can also be pronounced as sh sometimes, but this is rare. It is most often found in adjectives ending in -cious, such as conscious, precious, ferocious, etc, and also in adjectives ending in -cial, such as special, artificial, crucial, social, etc. One major exception where c is pronounced as sh is the word ocean.
There are many other exceptions to the above rules. You will learn them as you go.
As Jim points out, an excellent rule of thumb is "Except for ci, ce, and cy, it's pronounced as a k." With the exception of ch, of course.