how to update my iPhone4 iOS 5 or later?

You follow the instructions in the support article you linked to to get here.

plug into iTunes

Once you have iOS6.1.3 you will find the option to update over the air.

Apple only updates to the latest iOS level hence you will get iOS6.1.3

I realize you marked Peter's post as "solved", but if you follow those instructions, you will lose ALL of your data.

You need to follow the instructions in that support article. The update to iOS 5.0 & higher is an erase/restore deal.

You do

.Apple only update to the latest available iOS in the case of the iP4 that is 6.1.3