How do I download iOS 5.1.1 to my iphone 4?

You don't. You can only upgrade to the most recent iOS, in this case 6.1.3.

If your iDevice is using a version of iOS lower than 5, you will need to use iTunes on your syncing computer to perform the upgrade. Use the Apple link below as a guide for the upgrade.

http://support.apple.com/kb/HT4972

Also read the instructions from the section entitled "Update your device using iTunes" at the link below.

http://support.apple.com/kb/HT4623

Information regarding transferring purchases from your iDevice to iTunes on your syncing computer can be found at the link below.

http://support.apple.com/kb/ht1848

iOS is at 6.1.3 so that is what you can iPhone 4 update to.