After awhile you will falls down to the first cave where is marked by the wood block and a torch (Can be seen in the images below). An tipis remember this place to easily navigate your position if you lost in this cave system. From the marked point enter to the cave and go to the left side, and soon you will see 2 gold blocks and first 7 diamonds by continue to the right side.
That is good sign, the remain diamonds will be find by starting at the marked point. In there you need destroy the wood block and following the path until reach to the second cave system. In here you must find a room with the lava marked it with some things like torches it will be useful in the future. Then get back to where you were digging and dig straight down until you reach a diamond block. But careful if you digging too deep you will fall down to the lava. Walk over other rock blocks destroy them and lots of diamonds blocks surrounding can be found.
Searching careful the second cave system to find more diamonds. Good Luck!!!!