How to calculate the induced drag coefficient?
There's no way to calculate $e$ without using computational fluid dynamics (CFD) since it involves the calculation of complex three-dimensional flow interactions with the wing geometry (lift loss due to wingtip vortices).

For most aircraft, 0.8 is a pretty good estimate, so this is probably the value you're expected to use. If you need a more accurate number for your particular problem, you'll either have to know the specific aircraft model (in which case you would likely have to calculate $e$ given $AR$ and ${C_D}_0$, $C_D$, and $C_L$ for a certain state) or be given a number to use for the problem.