How can I tell apart an Airbus from a Boeing?
I like to train being able to determine the precise model of an aircraft.
I first try to tell if it's a Boeing or Airbus, and then I look at other details to determine the model.

The idea is to learn several differences :


cockpit windows shape (Boeing has an very specific angle) ; 
nose shape (pointy nose on Boeing, "fat nose" on Airbus) ;
wingtips (winglets Boeing, fence Airbus) ;
number of engines (A340, B747, A380 have 4 engines, all others have 2) ;
gear.


Since there are already nice answers describing most of these points with pictures, I will focus on the gear to add a new item to the list.

Landing Gear

Looking at the gear adds a new hint. Some landing gears are unique, which means that only looking at them will be enough to determine the precise aircraft type. These very specific gears are :


B777
B747
A340 (2 different kinds for this aircraft only)
A380


It's not worth to look at the nose wheels, because there are always 2. But the main landing gear is helpful.

I made a gear cheat sheet to help me learning them.



Once these differences have been learned, the key is to use several of them to crosscheck and ease and speed up the recognition.
For example if I see the gear

   2
2*2 2*2


I will then check the cockpit windows to determine whether Boeing or Airbus.
If it's Airbus, I will know it's very likely to be an A330! If it's Boeing, it will be harder since there are still 3 different aircrafts. If I want to be able to distinguish between them, I can learn new specific hints for this purpose.