As long as sunlight is hitting the dirt, some grass should grow eventually.
 
I think it has to be sunlight, though; torches/glowstone/fire won't work.

water

You need a connecting block that has grass on it as far as I know, so I guess a dirt staircase should work.

Sogeman and Soylent speaks truth.
You need blocks connected to grass covered blocks. They can be on top of them or beside them or anything, they just need to be connected to them. 
You also need sunlight to trigger the grass growth.
 
You should build a small marina with boats that you can hop into and ride down the waterfall.

Once it started growing you don't need sun anymore. I've seen a video where someone grew grass down into a cave.

Oooh thanks guys, I was kinda curious about this too. Now my sky island on top of my mountain fortress-tower can match the glory of my giant mech. Goddammit, I love this game.