Barbarians in Civ IV are pretty easy in general. You really just need to be prepared for them. Make sure that your first warrior defends your capital from the beginning. If you start with a scout, use the scout to explore and build a warrior first. This will also help you if you decide to play multi-player. Your next build should be another warrior or archer if you have researched archery or now build a worker or build a scout to explore. If you started with a warrior and you have techs or will have techs to improve the land by the time a worker is finished such as agriculture, wheel, and mining, then build a worker first. Make sure that you build a scout when you can though to explore if you did not start with one.
Once you have at least two warriors and a worker, it is time to consider building your first settler. Since you are having trouble with barbarians I might even wait until at least two archers before settling the next city. Hopefully by the time you are getting ready to found the second city, bronze working has been researched. This will allow you to see where the copper is. This is not essential but it is a pretty high priority early on. Having axemen will help you beat off barbs without any sweat. The other thing is that with bronze working, you get slavery which allows you to whip units for defense when that barb threat arrives and whip buildings. It also allows you to chop forests to quickly produce settlers, buildings, and units.
The other techs to make a priority especially if you have pigs or cows is animal husbandry and the wheel. This will show you where horses are. With those two techs and a hooked up horse pasture, you can build chariots. Chariots get a +100% against axemen in the expansions and absolutely destroy barbarian axemen.
When you send out your first settler, escort him with a warrior or preferably an archer and best of all if you're playing on an expansion use a chariot. It slows the settler down unless you use a chariot or scout but it will be much safer from anybody who decides to attack you. Try not to make your second city too far away from the capital. This will allow you to be more consolidated and make it easier for you to defend your empire. Preferably, build your second city near copper or horses if your capital does not have access to either. If you don't have either one near you, iron working will be something you will want to research sooner than later. Build a road between your two cities to allow for fast movement and a trade route. It probably is a good idea to escort your first worker with a warrior just in case. You probably will also want your capital to build another worker. Your second city should probably build a warrior, archer or axeman first off to give you some flexibility or a building such as an obelisk (monument), granary, or barracks.
Continue to expand in this way until you have five cities ideally. Archer-Settler and then go settle another city. Build a worker from the capital and have him build a road to the new city and improve it. Occasionally build some units to defend your empire and some buildings. Finding the balance is the key. Try to have a unit defend your key strategic resources and/or food sources. If a barb threat emerges that you aren't prepared for, quickly change production to an axeman,archer, or chariot and whip it to defend off the barb threat. But with the strategy I laid out for you, your cities will all at least be protected by one warrior or an archer. The worst that should happen is that the barbs might pillage an improvement or road but you should be able to quickly neutralize the threat. The only real way to get rid of the barb threat entirely is to settle the land and use your culture to expand your borders.
I hope this helps you. Good luck.
Once you have at least two warriors and a worker, it is time to consider building your first settler. Since you are having trouble with barbarians I might even wait until at least two archers before settling the next city. Hopefully by the time you are getting ready to found the second city, bronze working has been researched. This will allow you to see where the copper is. This is not essential but it is a pretty high priority early on. Having axemen will help you beat off barbs without any sweat. The other thing is that with bronze working, you get slavery which allows you to whip units for defense when that barb threat arrives and whip buildings. It also allows you to chop forests to quickly produce settlers, buildings, and units.
The other techs to make a priority especially if you have pigs or cows is animal husbandry and the wheel. This will show you where horses are. With those two techs and a hooked up horse pasture, you can build chariots. Chariots get a +100% against axemen in the expansions and absolutely destroy barbarian axemen.
When you send out your first settler, escort him with a warrior or preferably an archer and best of all if you're playing on an expansion use a chariot. It slows the settler down unless you use a chariot or scout but it will be much safer from anybody who decides to attack you. Try not to make your second city too far away from the capital. This will allow you to be more consolidated and make it easier for you to defend your empire. Preferably, build your second city near copper or horses if your capital does not have access to either. If you don't have either one near you, iron working will be something you will want to research sooner than later. Build a road between your two cities to allow for fast movement and a trade route. It probably is a good idea to escort your first worker with a warrior just in case. You probably will also want your capital to build another worker. Your second city should probably build a warrior, archer or axeman first off to give you some flexibility or a building such as an obelisk (monument), granary, or barracks.
Continue to expand in this way until you have five cities ideally. Archer-Settler and then go settle another city. Build a worker from the capital and have him build a road to the new city and improve it. Occasionally build some units to defend your empire and some buildings. Finding the balance is the key. Try to have a unit defend your key strategic resources and/or food sources. If a barb threat emerges that you aren't prepared for, quickly change production to an axeman,archer, or chariot and whip it to defend off the barb threat. But with the strategy I laid out for you, your cities will all at least be protected by one warrior or an archer. The worst that should happen is that the barbs might pillage an improvement or road but you should be able to quickly neutralize the threat. The only real way to get rid of the barb threat entirely is to settle the land and use your culture to expand your borders.
I hope this helps you. Good luck.