Get FRAPS or some other tool to display the frame rate and monitor the effects of your changes.
There are a quite some things you could try to do: reduce the graphics settings play at a lower resolution
use the strategic view (doesn't help as much as one would think) play on smaller maps don't zoom out as much (as Oak already said) win before the modern age
install the latest graphics drivers
If you're talking about the time between turns, you'll be happy to know that the next patch is supposed to significantly reduce that time.
You did not write your exact specifications of your computer, Civilization V is a pretty resource-hungry game, you'll need a relatively new and powerful CPU and GPU to play it at decent settings.
gaming.stackexchange.com/users/4103/Mad Scientist
Quick Combat and Quick moves make a difference in the late game.
Evidently, AI moves/fights at the animated on-screen unit speed, even in areas that are fog-covered or have not been revealed.
Switching this option reduced my turn wait-time by half.
Worth a shot for anyone.
gaming.stackexchange.com/users/30934/user30934
I found there were two video options that made a massive difference to the game's playability for me: Terrain Shadow Quality set to Off in video options completely got rid of the lag for me in the map.
Leader Scene Quality set to Low
stopped the diplomacy screens from loading slowly
I assume that different setups will have different optimizations, but given that you have to restart the game every time for every video change I'd recommend trying them first.
I was able to play at a high resolution with 20-30 fps, which doesn't make the map feel jerky when scrolling around.
To find these I installed FRAPs to watch the FPS and started by turning everything down to the lowest setting and gradually re-enabling everything.
Nothing had a noticeable lag effect apart from the Terrain Shadow Quality in the map.
gaming.stackexchange.com/users/28472/Matt M
CTRL +
G:
I find removing the grid lines improves the game speed dramatically in the late game.
CTRL +
R:
Removing resource icons.
gaming.stackexchange.com/users/10223/Valamas
I was having some horrible slowdowns on two different machines during later eras.
For me the solution was to to add both the save directory (My Documents\My Games\Sid Meier's Civilization 5) and the game directory (Program Files (x86)\Sid Meier's Civilization V) to AVG Resident Shield's exclusion list.
The game still has some memory leakage that slows it a little over time
but i'm no longer getting the 1.5-2 minutes per turn
i was getting
(now the max is like 30 seconds).
gaming.stackexchange.com/users/10913/binstar
Civilization V can be a very demanding game when it comes to your computer.
one way you could improve the speed is by closing out of other programs and also turn down some of the graphical settings.
Also the map size and the amount of leaders you are playing with can also effect your preformance.
gaming.stackexchange.com/users/10987/Huffy
The strange thing is...
Everybody says that Civ5 is demands many of your computer.
But Civ5 does not completely uses your system.
This is mostly normal, because many new games like: Battlefield 3 & Farcry 3 demands between 80%&100% of your graphics card.
I monitort my system in Civ5: GPU's between 30/40 % (sli)CPU @ 18%MaxMemory @ 19%
Max... and no
..
the cpu usage doesnt increase if i press end-turn.
Why does civ5 asks so few from my system?
Ok OT:
Few tips that helped me... 1.Disable
Barbarians 2.Start
a game without City-states and @ to compensate 2 extra civilizations.
gaming.stackexchange.com/users/44186/Elmar
I have pretty decent hardware and I run many games on it. But Civ 5 is unacceptably slow when it reaches an advanced stage where it shows the whole map and there are many units.  I tried to monitor the CPU and memory and I couldn't find the bottleneck. I run it in a fast SSD and I didn't monitor my GPU.  I noticed a speed improvement when I changed from DX10/11 to DX9. But the performance isn't acceptable yet.
How do I improve Civilization V's performance?
gaming.stackexchange.com
<civilization-5><performance>
gaming.stackexchange.com/questions/17018
gaming.stackexchange.com/users/3375/Jader Dias
Get a tool to display the frame rate and reduce the graphics settings. You can also install the latest graphics drivers. It is a good idea to get FRAPS to tell you the frame rate so you can monitor the effects of your changes. Reduce graphics settings or play on lower resolutions. Use strategic view, install the latest gpu drivers , lower terrain shadow quality and leader scene quality or removing resource icons.
Users suggest multiple solutions to the issue.