There's very few methods to do what you're asking.
Here are some suggestions:
1. Clean hard disk on your game hard drive and also OS (windows, mac etc) hard drive. Free up space till they're no longer in the red.
2. Run a disk defragmentation program like Smart Defrag on your hard drives, this can improve performance. Don't use the default windows defragger, it's pretty bad and slow.
3. Play in strategic view, or switch to it before you end your turn.
4. Run the game in windowed mode. If you have windows XP or Vista, try running the game
5. Close as many other progams and end as many non-essential processes as you can before starting Civ V.
6. Open up your computer and gently clean as much dust etc out of it as you can, especially around the fans. A PC that runs cooler is a healthier and faster PC, generally.
7. Get rid of any spyware or viruses that might be on your PC.
These methods might offer you very minimal improvements, if anything - but try them anyway as it can't hurt.
I know you asked for non hardware methods, but you would very surprised at how cheap it is to buy a little extra RAM and what a huge effect that can have on your speed. I upgraded from 2GB to 4GB (really cheap, less than $40) and even though my system could only use 3.5GB (32 bit system) it made a really noticable improvement.
