Obsidian farming refers to methods to obtain large quantities of obsidian. Obsidian does not spawn naturally with the terrain (except in the End), instead being created by natural events or player action.
The simplest method is to pour water over lava source blocks, either in a naturally-occurring lava pool or transported in buckets. A more advanced (and renewable) method is to take advantage of nether portals being created when no destination portal is in range or the recreation of the 5×5 platform when using the end portal.
With a beacon, the Haste and Haste II effects can be used to reduce mining time further. Using Efficiency V without a haste effect, it takes about 2.25 seconds to mine each block, resulting in being able to mine approximately 26.7 blocks of obsidian in a minute. With Haste, this is reduced to around 1.85 seconds per block, or 32 blocks in a minute. Haste II further reduces the time to mine each block to about 1.6 seconds per block, or 38 blocks a minute.
In the Overworld lava primarily occurs deep underground, but can sometimes be found in small lakes at or near the surface. Lava springs typically contain only a single source block, which is not particularly useful when the intention is to "farm" obsidian.
Lava is much more plentiful in the Nether, but as water cannot be placed there it is necessary to bring it back to the Overworld in buckets for conversion to obsidian.
Lava drenching is not a renewable method of farming obsidian, as lava source blocks are not a renewable resource.
In-place drenching and mining
The simplest method for obtaining obsidian is to find a lava pool, pour water on it, and then mine it with a diamond pickaxe. Seeming natural deposits of obsidian in the Overworld were created by water falling on lava in this way.
Note that the layer of obsidian thus created will often have more lava underneath, which will frequently destroy the mined blocks before they can be collected. The solution is to mine a single block (which may be a stone or dirt block next to the obsidian pool) and place water in the hole. Then when the obsidian blocks adjacent to the hole are mined, water immediately flows into the space to drench the lava beneath before it can burn the mined block. If you are standing in the water to mine the adjacent obsidian, be careful to move the water source block periodically so it doesn't reach its limit and push you or items into undrenched lava.
Obsidian structures such as Nether portals may be created in place, without the use of a diamond pickaxe, by placing a layer of lava source blocks in a mold, drenching, and then repeating for additional layers. Dirt or another easily mine-able block is typically used for the mold.
A much faster form of obsidian creation for large structures can be made by building "scaffolding" to create a frame two away from the desired location of the obsidian and using this to create an artificial waterfall a square away from where Obsidian is wanted. It is then possible to "float" inside of the waterfall and create large amounts of obsidian by placing buckets of lava next to it. This has the advantages of not needing to be built up and have the water moved with every new row, and allows the maximum of 36 buckets of lava to be converted at once. Care should be taken to remain clear of the row where obsidian is being created, however, as the solid block created can suffocate the player.
To farm obsidian using Nether portals, travel to the Nether and build a second portal at least 16 blocks away. Preferably, do not make the distance much more than that from the arrival portal. Using this second portal will bring you to a newly spawned portal in the Overworld just over 128 blocks away from the original portal. Mine out the new Overworld portal (or the old one, if you'd rather). When returning to the Nether, you'll find both portals are still active and using the second will spawn another portal in the Overworld at or near the place where the mined portal had been.
A single portal may be also used: one player travels to the Nether, then the second destroys or deactivates the portal in the Overworld. The first player then uses the Nether side of the portal to return to the Overworld, which will create a new portal nearby. This could also be done by a single player using some mechanism, such as dispenser placing water or lit TNT timed to deactivate the portal just after teleportation.
Another single-portal method is to travel to the Nether, mine out the Nether side of the portal, stash the obsidian in a chest, and die. When returning to and using the Overworld side of the portal, a new portal will be created in the Nether.
In all cases, be sure to maintain a 4×4 area of flat ground (with at least 4 blocks of air above the entire area) near the location of the destroyed portal, either by filling in the holes left by mining out the base of the portal each time or by leaving the four base blocks unmined. If this is not done, you may suddenly find the newly created portal is in a cavern underground because there is no longer any valid location for a portal to spawn on the surface. Also, be sure no other portals are within 128 blocks in the destination world or you will be taken there rather than having a new portal created. See Nether portal#Portal Search and Creation for details on the spawning algorithm.
The End platform
When using an End portal to travel to the End, a 5×5 platform of obsidian is created for you to appear on. If the platform is damaged, it will be recreated. However, getting back requires killing either the ender dragon or yourself.
When the dragon respawns, so do the obsidian towers surrounding the exit portal. These towers extend quite high and reach down to y=0.
Automatic Obsidian Generators
The biggest problem with obsidian mining is the mining part - even if you use the best pickaxe, it takes 2.5 seconds to mine a single block. Various methods have been used (and patched) to break obsidian blocks automatically, especially with the appearance of the wither which is capable of breaking obsidian blocks with its attacks.
One of the first designs used the wither to break portions of the 5×5 obsidian spawn platform in the End, and regenerating it with a sand generator that pushed sand through the end portal situated in the overworld. This method was patched however when the wither was made to shoot blue skulls that were capable of breaking any block. The following video is an explanation of how this method works. WARNING: this method works only in Minecraft 12w36a and several earlier versions.