Problem downloading an app? Not enough space?

I recently bought The Dark Knight Rises but I can't download it because my iPhone apparently doesn't have enough space to download the game. I downloaded the game on the iPad and it's 1.4 GB. I have about 1.9 GB left and I don't want to delete my biggest app (Injustice). I know that I need about twice as much space to download it normally by using the "Purchased" menu and downloading it from there but I read somewhere that I can download it onto my computer using iTunes and then sync my iPhone to get it. I don't know how to download it onto my computer and then sync my iPhone.

Just downloaded the itunes to your computer. Plug in your phone and then sync. But make sure you sign in into your itunes account on your laptop. The sync is automatically.