I have five players. A couple sessions ago, I noticed I had five different colored "tiddly winks" in my old dice bag. Those chips are now the inspiration markers. If a player has it, they have the chip. If they don't, the chips sit right by my dice, so I see them all the time. Someone had mentioned, in another thread, having a specific "inspiration die" that the players need to grab and roll, when they use inspiration. I'm pondering the idea of something similar, but finding five uniquely wild-colored d20s to use instead of the chips. The PC would always use that die, but would also have the opportunity to see what the result of granting disadvantage to an opponent was, too.
As far as when to give out inspiration, I guess it depends on my mood. I look at inspiration as a toy mechanic designed to promote fun, however your group defines it, so I kinda roll with whatever the mood of the table is (or what I want it to be) that evening. Some nights, that means that the best in-character zingers get inspiration. Other nights, it's acts of heroism, or a great idea, or playing to back story, or just stepping up level of play (for my newbie daughter, especially). Basically, it's whenever the player does something that catches my attention in a positive way and improves the entertainment value of playing the game (i.e. no inspiration for disruptive, but hilarious, out-of-character jokes).