How is an payment transaction in bitcoin executed?


Most blockchain literature provides descriptions of miners solving problems and if successful adding a new block to the existing chain of blocks. There are nowadays other approaches with a similar procedure.

However it is not always clear how a payment from A to B is executed. Take the following example: A orders a payment of a certain amount of bitcoins to B; who makes sure that B receives his amount of bitcoins and where can the addition to B’s account be ascertained and similarly the reduction of the account of A?