How to download IOS 8.1.1 on an iPhone 4s?

So I have an iPhone 4s and like 4.7 GB left in my storage. And when I try to download iOS 8.1.1 it says like "Estimated time 13 hours" So I leave my phone plugged in and on all night and all day and it says "Error downloading" How do I download it? And I don't understand how to download with iTunes so can someone explain that too?

I have about the same GB left. I was able to do it in about 5 minutes maybe less. It's very likely that it's just your internet provider and speed. If you want to do it on iTunes. Plug it your phone and wait till iTunes reads your phone. You will see your phone ands it's information pop up on there. Then it should let you know that there's a update or you can see very easily that there's a check for update or Software Update button. Press it and follow the instructions. It's simple.