IAS 39 requires many financial instruments to be measured in the accounts at fair value. It requires others to be measured at amortised cost. IAS 39 divides financial instruments into various categories ( CFM16055). These categories determine the method of measurement used.
Fair value is the amount for which an asset could be exchanged, or a liability settled, between knowledgeable, willing parties in an arm's length transaction.
The amortised cost of a financial asset or financial liability is
You work out the amortisation using the effective interest method.
This is a method of calculating the amortised cost of a
financial asset or financial liability, and of allocating the
interest income or interest expense over the relevant period. The
effective interest rate in a financial instrument
is the rate that exactly discounts the cash flows associated with
the instrument (either through to maturity or to the next
re-pricing date) to the net carrying amount at initial recognition,
i.e. a constant rate on the carrying amount. The effective interest
rate is sometimes termed the level yield to maturity (or the next
re- pricing date), and is the internal rate of return of the
financial asset or liability for that period.
There is more about computing the effective interest rate, with an example, at CFM16025a.
CFM16025b gives an example of measuring a financial asset at fair value, and at amortised cost.