You can make settlers build roads, irrigation, etc. in one turn (instead of the normal 2 - 12). Make the settler unit build a road or irrigation. When, in the same turn, another unit higlights, go back to settler, and click on it. Now the R or I disappear. Make the unit build a road or irrigation again. Repeat this a few times until the desired advancement is build.

Move ships long distances in one turn in pairs by passing a cargo unit back and forth.
Move land units long distances by having them go on sentry duty in a city and reactivating them the same turn.
Have ships 'steal' loads. A ship will load as many units as it can when it leaves a square, including at sea when another ship just ended its turn at the samespot.

Move your units as usual. Save the file. Quit Civ and reopen this file. Now you can move your units again, while the year hasn't been changed. However the amount of money, etc. hasn't been changed yet. This can be handy if barbarians arrived and you can't reach them with your army in one turn.

If you want to buy a wonder/unit/improvement (a rush job) the price per resource is different. If you want to buy a wonder immediately for the cheapest prize, do this:

Select the cheapest unit or improvement.
Buy it. This is quite expensive because the price doubles when you're resource box is empty.
Now select the most expensive improvement.
The price per resource for improvements is cheapest. Then come the units, and the price per resource for wonders is the expensive.
Buy it.
Now select the desired wonder, and buy the remaining resources. This proces can save up to 50% of the costs. That's a nice amount given the price of wonders.

Use a diplomat or caravan to enter a square a military unit could otherwise not reach and then occupying it in the same turn with the military unit.

Move ships long distances in one turn in pairs by passing a cargo unit back and forth. Move land units long distances by having them go on sentry duty in a city and reactivating them the same turn. Having ships 'steal' loads. A ship will load as many units as it can when it leaves a square, including at sea when another ship just ended its turn at the same spot.

1. Wait until your screen saver shows up. (This cheat seems to only work with After Dark or Disney AD screen savers).
2. Move the mouse and see the whole map for a few seconds.

1. Click on the fortified or sentried unit.
2. Click on its icon in the small info screen that appears. It should change from greyed out to its normal colour, and the piece will be active.

After gaining gunpowder and combustion your old barracks get obsolete and you have to build new ones. The computer disposes them automatically. If you sell them just before they get obsolete, you will still get £40 for each.

If you want to have a fast connection between two continents, you can put a boat (or more) between it, and put it into sentry. Now board a settler. Now You can build a road just as if it was plain land. The road disappears as soon as the boat moves. You can still use the settler. If you want to have a connection between two oceans close to each other, you might want to let your boats travel over land. That's possible. Just build a city (or more) in the land between oceans. Now you can move your boat into the city, and move it out to the other ocean next turn.

In the beginning build at least 4 militia units. Use two to explore the land and two to protect your city. Quickly develop pottery, barracks, and pursue writing before any other cultural advances. Writing will help you get ahead of your competition. Be fruitful and multiply. Building a few cities in your first millennia will help your expansion efforts in the future. After you've built a few cities, provide a defensive perimeter around those cities. Don't let anything get through. Don't develop every square around a city early on, you can do that later.