Other things like music and photos might be taking up room on your iPhone. If you don't want to delete those items, you might want to do the update using a computer. That won't require 3 GB of space on your iPhone.
Try the steps in this article: http://support.apple.com/kb/HT4623
You can also try importing your photos to your computer: http://support.apple.com/kb/HT4083
I was having the same problem (my available space was down to zero). If you have copies of your pictures and music library you might try deleting them. I was told that I had to have 7GB of space available to do the backup, which is the first necessary step when installing iOS 7. I finally removed enough and it worked.
[Note: It's now 7.0.1 and I'm sure it will be updated frequently for awhile as we guinea pigs report all the glitches and crashes.]