As a chronic MAF-sufferer (limited to DoC though) I would like to add some additional tips to this thread, written in a way so that less techy people will also get it.
Graphics
Everything on low. No animations. No anti-aliasing. The lowest resolution possible. The bare minimum. Also play on windowed-mode (explained below)
General
Look in task manager and see if there are any processes that take a lot of memory and that you can switch off. Also look at the bottom-right segment of the taskbar, to see if there are any background programs running. Especially google drive is heavy on memory. Like Leo said basically. I also use airplane mode on my laptop, which turns off bluetooth as well.
4GB patch
Download the 4GB patch, run it, and use its menu to open the BtS exe. This has been mentioned in other threads but just for completion I decided to add it here:
https://ntcore.com/?page_id=371. This only works for 64 bits systems.
IncreaseUserva
Run command prompt (search for cmd) as an administrator. If you have a 32 bits system (God have your soul), type bcdedit /set increaseuserva 3072. If you have a 64 bits system, like most people nowadays, replace 3072 with 4096.
CivilizationIV.ini
Search for this file an open it with notepad (this should be the default program). Change the following settings.
Memsaver = 1. When you have selected this option, never minimize the civ window nor cycle through windows using either Alt-tab or windows-tab, as this will cause the game to crash.
FullScreen = 0 (to enable windowed mode)
DynamicUnitPaging = 1, DynamicAnimPaging = 1.
AutoSaveInterval = 1. This option is really optional, I just do it so that I only lose one turn max when I crash. It kind of affects performance but to me the benefits outweigh the drawbacks.
DisableFileCaching = 0, DisableCaching = 0.
Enable logging as explained in the Bug Reports Thread:
LoggingEnabled = 1. This is so that it keeps the crash logs (in the folder Logs) which indicate what is causing the crash, or upload it and get help (in the Bug Reports thread).
Loading saves
Whenever you load a save, rather than starting a new game, be aware that this is the point at which the game is very sensitive to crashes. Any abrupt camera movement or too quick selection of units and stuff can cause the game to crash. I recommend that, when you load a save game, you just wait for a few minutes while not touching anything. Like, take a bathroom break or scroll a bit on social media. Maybe get a sandwich. Then, when you start playing, just let the game cycle you through the units and try to avoid moving the camera yourself at all cost. After a few turns, the game will have left this sensitive stage and you can be more relaxed. Generally avoid playing late-game civs. It's sad, but that's the way it is.