How are bitcoins put in to circulation?
Let me answer your questions out of order:


  What's the point of bitcoin mining / how they are put in to circulation?


https://bitcoin.stackexchange.com/a/3201/2306


  what happens if my computer is destroyed. Are those bit coins gone forever?


Yes.


  Wouldn't this cause the supply of bit coins to go down overtime until eventually there are very few bit coins left?


Yes.