I think there are quite a number of tips to remember, but the best ones to always remember are:
1) Attack with alot of attacking units, NOT defensive units (unless you've got Infantry onwards). It's important to OUT NUMBER the opposition.
2) Try and get a leader, by eliminating enemy units (excluding barbarians) with elite status units.
3) Use stacks of Artillery* or cannons (10 or more) to knock an enemy's health bar down to 1 point. This is especially effective at weaking city defenders. The more artillery units you have, the better, as they often 'miss' the target - don't forget to put a few defending units with the stack, to prevent the whole lot being captured.
4) If you're on an island/continent, use your ships to sink incoming transports and carriers.
5) Use Cruise Missiles to sink ships and bombard cities or enemy units. They're cheap & quick to build and they NEVER miss!
6) ALWAYS have a strategy*. Plan for a reasonably quick win, either to destroy a number of cities, or to capture an important resource or Wonder in a city.
6a) Part of that stategy should be to destroy roads that lead to a enemy's resource square, eg. aluminium or iron. That will limit their production of modern units to lesser attack units, that you can easily destroy.
*This is a really good tip.
