How to diagnose card issues?

[Pawnless Endgame]

I've got a perfectly good computer, not doing any fault-finding, but I am interested to know how to tell if a graphics card is on its way out. People mention on here speak of artifacting - what does it look like on the screen when a card artifacts? Does artifacting point to the GPU itself or its memory? I would appreciate seeing examples of different types of graphics problems, then perhaps have the topic made into a sticky / troubleshooter?

I know for sure that 1-long + 3-short Morse Code at POST indicates a bad card.