You can find diamonds under the 10th level, where lava spawns, if you don't know how to find the 10th level just dig down to bedrock in a staircase way then count about 10 or 9 steps up then just start digging around there (It may take a LONG time) but eventually you will find some diamonds, you could also go look around on YouTube there are plenty of tutorials on how on how to find diamonds.
Usually diamonds are around the same level as lava pits. I would recommend searching ravines or large cave systems, and if your desperate, dig down. Always dig down two block spaces to prevent falling into lava and dying. If you see gold, don't give up. start a mine and dig around a bit. You'll find diamonds eventually, so mine on!
Dig straight down. There should be some near the bottom (core) of earth. To get up to the surface, jump and then place a block down. You will get up(: bring about 40 blocks of dirt with you so you can get up