How do I create floating Islands and lava columns?

Floating islands are generally natural formations that are made on the map, however you are free to create them yourself.

Basically, any block outside of Sand and Gravel do not actually obey gravity, and simply stay in place when the block below them is destroyed (or when placed adjacent to another block with nothing underneath it). Using this simple concept, you can create your own floating platforms by first building using a grounded scaffold, and then destroying the scaffold.

If you "sneak" (check your configuration for the key) then you will not fall off the edge of any block, so you can place several adjacent blocks while on top of your platform by looking over the edge of the platform and placing a block. This will allow you to create vast floating platforms.

As for lava you need a Bucket crafted and a lava source block, that is, a block of lava that isn't "flowing". You can than harvest the lava source block while holding the bucket and right clicking on the lava source block. You can then place this like any other block (and lava will start to flow from the source block).

You can manipulate lava via buckets, which work on lava just like they work with water. Right click to collect a lava source block,

For floating islands, ducking is very useful (you won't fall down while you duck, which makes it easier to build horizontally.