A cave is a place where you can find many resources or it's just a little room. Sometimes you find them on the surface, others are buried underground. These are the easy ways to find them (else than finding them by just digging rock)
Surface Cave Entrance
Usually, when you go exploring the surface, you might find cave entrances. Watch out though, mobs could be lurking at the entrance. This method is known as Cherrypicking, but you can also use a good strategy called strip mining.
Common entrance for a cavern.
Common Mob(s) in the cavern (Spiders as this picture shows)
Resource veins
As caves have a lot of resources, you can enter a cave by digging resource veins. When digging veins you may hear mob sounds which means there is a cave nearby. Be careful though or you could come face to face with a creeper!
Dirt/Gravel veins
Caves have dirt/gravel veins on them depending on how big they are. A big cave has many dirt/gravel veins and a short cave might have only one. Even if you find no cave by digging these, you will have created a cave-like room, or it may mean that a cave is nearby. Remember: If you find a dirt vein near the surface, don't dig it because you will end up in the surface. It is more suggested to dig a dirt vein if it's 15 blocks below the sea level. It is highly likely that you will find rare or semi-rare materials buried in or around dirt and gravel veins. Be sure to fully excavate these veins but exercise extreme caution as well, you may discover dark caves, mobs, lava etc.
Example of a Gravel vein to a entrance into a cave.
Dungeons
Dungeons are places where monsters generate and there is loot in chests inside of them. Most dungeons are connected with caves. However, dungeons are quite rare and are not an easy way to find caves as most are found in a pre-existing cave and very few are found on the surface.
(More detail on Dungeons can be found here)
Ambience
Another way to find caves is to try and find spots where you hear strange noises that indicate dark places. if you were to hear a zombie, spider, skeleton or slime you should dig to it because you might find a whole new cave system!
(More detail on Ambience can be found here)
If a cave ends and you dig through the wall you MIGHT find another cave system. if there is found a dirt wall at an end of a cave there is a very high possibility that there is a cave there
F3 Key
Pre 1.8, you could press the F3 key to show a mob's ID. This would show the location of a mob in a cave (when not on Peaceful); if you dug towards the mob, you would have most likely revealed a tunnel system that the mob was in.
Pistons
This is a simple and effective technique. Simply place down pistons facing the wall(s) you are looking for caves behind and power it with a redstone torch. If there is an empty space within 12 blocks the piston will push. Simply dig in that direction and you should find a cave! Courtesy of Rabid_frog (MC Name)
X-ray texture packs
All texture packs which edit an opaque block so that a part of it/ all of it is transparent can help find caves. When the block is looked through, it shows every air pocket above and underground. However, this is cheating.
An album of images can be found here :http://imageshack.us/g/62/20110709113322.png/ The example see-through block is white wool. Can someone do all the upload pictures and things because I'm really bad at that sort of stuff? Thanks Creeponyou31 10:45, 9 July 2011 (UTC)Creeponyou31