Finding difficulties in memorizing things? Let's learn it in some easy ways.

To memorise the direction of induced emf according to the Lenz's Law, assume the loop to be a just like human. 
When he has money (magnetic flux) and he is offered more, then he declines the offer. 
When money is taken away from him, he tries his best to get it back.

(a) If a north pole of magnet is moved closer to a loop, the loop will create a North Pole (N) to scare away (repel) the magnet (cause of increase in flux through it). 
(b) And if the north pole of magnet is moved away from the loop, the loop will create a South Pole (S) to tempt (attract) the magnet (cause of decrease in flux through it).

To remember the direction of motional emf in a conducting rod of length l, moving with constant velocity v under a magnetic field $$\vec{B}$$ we simply apply Lorentz Force on a free charge carrier inside the rod.

The expression of the energy required to build up the current I in an inductor L is analogous to the the (mechanical) kinetic energy of a particle of mass m. 
So L is analogous to m (i.e., L is electrical inertia and opposes growth and decay of current in the circuit).

To find the direction of induced current in Generator, read Generator as 
Gen-RIGHTER. 
i.e., we apply Fleming's Right Hand Rule.

Electromagnetic Induction