The hexadecimal system is a base 16 system, just as binary is base 2 and decimal is base 10. The same way that a binary system is more practical for hardware and software implications, hexadecimal is...
It's a bit like long division. The site that I linked below has a good explanation. You can also use specialty calculators, or the programming mode of the Windows calculator.
Because the system is based on counting in blocks of ten. A medium large number is represented as a number of thousands (10*10*10)plus a number of hundreds (10*10)plus a number of tens (10)plus some...