You can find Lapis Lazuli in a cave or a mineshaft, but im preety sure that you can't pick it up unless you have the 1.2.5 upate for it.
Below layer 32. It is slightly rarer than gold.
No, the only gems in Minecraft as of Beta 1.7.2 are Diamonds and Lapis Lazuli.
It can be found on levels 32 and below, but 19 is the optimal layer.
gold iron coal diamond lapis lazuli MAYBE emeralds
It is found in caves and can be requires when mining with a Pickaxe.
You can find it in caves and you must dig it with pickaxe (not wooden or stone pickaxe)
You can make the following: Lapis Lazuli blocks, and Blue wool To make Lapis Lazuli blocks L L L L L=Lapis Lazuli To make blue wool W L L=Lapis Lazuli W=Wool
You can make blocks out of it, for building with, it can also be used as a dye.
You can craft things with Lapis like: A Lapis Lazuli block, light blue dye, cyan dye, purple dye, magenta dye and blue wool. You can check out Minecraft Wiki for some help and tips.
Find and mine some 'Lapis Lazuli'. This is blue dye, and mix it with red dye, which can be obtained by putting a red flower into the crafting table, then put both the lapis and the red dye into the crafting table to make purple.
You can dye wool with it, or you can create decorative blocks of it using 9 pieces.
Lapis lazuli (the blue dye) cannot be crafted, but is mined from lapis lazuli ore, which can be found most commonly between 13 and 16 metres above bedrock level. Mining a lapis lazuli ore block with a stone or stronger pickaxe yields 4-8 lapis lazuli shards.
In order of most common to rarest: Coal, Iron, Lapis Lazuli, Gold, Redstone, Diamond, Emerald.