bpops:
I'm primarily a Prince player myself. I win most of the time, but I don't score all that well, either.
A couple tips...
1. Play the tutorial. You've played five or so games already, so I doubt this is necessary, but I've always found it helpful to at least fool with the tutorial a little bit in new games. Especially in RTS games.
2. There are a few fundamental differences between CivIII and CivIV so you can't rely too heavily on your experiences with CivIII to drive your strategy in CivIV. The two biggest differences are the subject of my next two points.
3. Expand carefully. In CivIV each city has its own City Maintenance cost. This cost is a function of how far your city is from your capital and the total number of cities in your empire. This is a significant difference from the 'corruption' model of CivIII, wherein your further flung cities usually displayed a drastic production/commerce lag. Because of these City Maintenance costs, it is easy to go broke early in the game if you hold too many cities. When warring early in the game be mindful of what cities you capture and what cities you keep. If the city you conquered is on a good piece of land with some resources around it, keep it. Otherwise, burn it. As you progress technologically, Courthouses and financial buildings can help offset the City Maintenance costs. A good rule of thumb is to be able to run your science slider between 70% and 100% for the whole game. If you dip much below that, you probably have too many cities without the requisite infrastructure (Courthouses).
4. Beware the Stack of Doom. The predominant strategy in CivIII was to build up a massive stack of the latest military unit, combine them with artillery, and take over the enemy. In CivIV the combat system is totally revamped. If a siege weapon attacks a stack, it can damage several units in the stack. So if your opponent has siege weapons, don't concentrate your military in very large stacks. Furthermore, use combined arms. Every military unit has some strengths and weaknesses. For example, the axeman gets a 50% bonus against melee units, and the archer gets a city defense bonus. Therefore, it is important to bring several unit types to war.
5. Focus your research. Pick some specific techs you want to obtain, and make beelines for them. For example, if I'm playing a terra map, it might be a good idea to beeline to optics for the Caravels and then to Astronomy for the Galleons so that you can find and colonize the New World. Depending on what kind of game you plan on playing there are usually large tracts of the tech tree that can go mostly ignored for much of the game. Research what you need and trade to fill in the holes.
6. Get a Holy City by either founding a religion on your own or by capturing another Civ's holy city. Then spread that religion, through missionaries, like wildfire. Combine that with temples and monasteries to produce a significant boost to your economy. Use a Great Prophet to build a shrine in your Holy City because a religion's shrine collects gold from every city in which that religion is practiced.
7. Specialize your cities. In general, I like to have two military production cities, one financial city, one cultural city and one Great Person city. National wonders, workers and land help determine which city should specialize in what. For example, cities with surrounding forests and hills should be military production cities. Cities with a lot of grasslands and such make as Financial/Great Person cities. Cultural cities should be between the two.
8. Use your workers to emphasize the city specialization. For military production cities, mine hills, create lumbermills and watermills, try to leave forests alone, and farm minimally. For financial/Great Person cities farm heavily and use windmills. A little bit of everything for cultural cities.
9. Use your National Wonders to further city specialize. You can only build two National Wonders in each city. In my military cities, I like one to have Heroic Epic and West Point, and the other to have Ironworks and Red Cross. For financial, I like to put Wall Street in a Holy City with a shrine. Your cultural city should have the Globe Theatre, and your Great Person city should have the National Epic.
10. Pick a victory condition to aim for and play to it. They all require fairly significant planning. For domination/conquest, build your military early and often, and use it to overwhelm your enemies as early as possible. For cultural victory, try to map out what three cities you want to focus on culture and build wonders and use great artists to increase their cultural value. Towards the end of the game, quit producing buildings and units in these cities and produce culture instead. For the diplomatic victory, foster strong relations with a few Civs (this will mean trading, often at a loss, and also giving help when it's requested), and get Mass Media first so you can build the UN. For the Space Race victory, get aluminum, build laboratories, and beeline to the Space Elevator. Doing all three of these things allows you to produce your Spaceship Components much faster than your opposition.
11. Play to the strengths of your Leader. If your leader is Isabella, she starts with Mysticism, and it might be a good idea to go for Polytheism to found Hinduism. If your leader is Caesar, it might be a good idea to try to get Iron Working early to hook up iron and produce Praetorians. If your leader is Bismarck, you might not need to research Animal Husbandry at the very outset of the game because of the Expansive Trait.
12. Play to the map type. If your map type is Great Plains, it might be a good idea to get Horseback Riding and some horses so you can create mounted units. If you're playing a Pangaea map, you might not need to worry so much about getting Optics and Astronomy. But on Terra maps, it is crucial to pick up Optics and Astronomy early, if possible.
Those are my big-picture tips...other more minor tips could be...
13. I like to pick up Bronze Working fairly early. Bronze Working allows you to chop forests for a production bonus. This helps immensely, especially in the early game to produce settlers. Get a worker, send him to a forest, set your city to produce a settler, and chop the forest. Using this process to create Settlers will help you produce them much more quickly.
14. Use your civics to your advanatage. If you are going for domination/conquest victory, you might want to run a Police State, Vassalage and Theocracy for the quick military unit builds, decrease in war weariness, and additional experience points for units.
15. You don't need every wonder. Tailor your Wonder building attempts to your victory type. Domination/Conquest? Go for Pentagon. Diplomatic? UN.
16. Build/promote your military to best counter the enemy. If the enemy will be coming with mounted units, build spearmen. If he's coming with Swordsmen, build Axemen. If he has tanks, build gunships.
17. Use artillery effectively. Most cities have a cultural defense bonus that is displayed as a percentage near the city name. Use artillery to bombard that number close to 0, and if there is a large stack in the city, use your artillery directly to attack it. This will cause collateral damage among some of the units in the stack. Your artillery unit will most likely die in the attempt, but it's worth it. Just keep cranking out artillery units. After bombarding defense close to 0 and attacking with a couple artillery units, it usually isn't to hard to take the city with a direct assault.
18. During the course of gameplay, you will see the computer make several suggestions on where to settle, how to improve the land around a city, and what to research. Do NOT be afraid to ignore the computer. Think about why the computer is making this suggestion, and if you don't agree with the reasoning, go your own way.
If you do even some of these things, you will be able to beat Warlord with ease.
Hope that helps a little.
-MM