I placed dirt blocks. I even cut tall grass and planted it in the hope that regular grass would grow from it, but it did not work. I don't know how to collect a grass block except on cheat mode. Is there a way to get a grass block?
Added (1). I have never heard of a silk touch shovel. How do you get it?
Use a silk touch pickaxe or shovel
Best bet is silk touch. To get it I suggest getting to level 30, get an enchanting table and surround the table with bookshelves 1 block away. You should see little symbols going into the enchanting table. I heard if it is dark you get better levels but I don't know if that is completely true. And save the game before enchanting either a pickaxe or shovel. Put a level 30 enchantnent on it and check to see if you got silk touch. If you didn't get it quit without saving and load it up again. Repeat until you have it. Once you have it use it to get a grass block. When you get the grass block put it where you want and I believe if you put dirt blocks around a grass block, the grass should spread.