The basic strategy is a progression from despotism to monarchy to republic to democracy. Some people (especially warmongers) will use different strategies. My basic rules of thumb:
- stay in despotism until:
1) most or all of your cities have some good irrigation/mining/roads infrastructure around them, and
2) you've expanded as much as you can without war
then switch to monarchy. Stay in monarchy until most of your cities are over 6 and some are 12 or over. From there you go to republic. Usually I don't go to democracy until I'm pretty sure I won't be getting into a war in the near future, and universal suffrage has been built.
Comparing the different governments in the civilopedia should help show why this works. In general, each new government allows greater maximum city development (+ science & wealth) but makes the cost of war and some basic maintenance higher. If you switch to the next government before your cities are sufficiently developed, the costs will outweigh the benefits. If you wait too long, you'll be missing out. Communism should rightly go in between monarchy and republic doesn't really fit into this progression because it appears so late in the game -- therefore it's usually used as a wartime-only government.
Hope that helps.
