Charlemagne starting tips (not for Conclave, haven't tried him yet in the 2.5.2 patch):
At the beginning you're going to be targeted by at least one faction, possibly two. Usually these factions include the Dukes of Aquitaine and Gascoigne and the Count of Bearn. Sometimes the German dukes get involved as well. Firstly, transfer the Count of Bearn and make him a vassal of his de-jure lord. This should calm them down a bit. Then position your excellent spymaster. If the Germans are involved position her there and tell her to scheme. German involvement in the revolt is usually very bad as it means you have to fight on two fronts, so you want to stop their plotting as soon as possible. The Dukes of Aquitaine and Gascoigne are harder to deal with peacefully but they're all in the same area. If they're the only participants in the faction, use your spymaster to dissuade one of them.
There's a fairly good chance that your spymaster will be successful, and after one of the main faction members drops out there usually isn't really enough strength left between them to continue plotting. If this doesn't happen you might also manage to avoid a rebellion, once you inherit your brother's lands those dukes can't really touch you. However, more likely than not there will be a faction revolt. If the Germans aren't involved it will be easy to crush. With the Germans it's a bit harder, depending on who you're dealing with.
Another early war that often happens is a revolt against Carloman. You hate Carloman but he's your ally, and when you inherit you don't want Middle Francia to be under elective succession. So if he suffers a rebellion (and you're not at risk of one yourself) join in and aid him.
Once Carloman is dead you will inherit his lands. This will probably bring you over your vassal limit and you won't have much cash to create duchies. So create a few of the biggest duchies (like Normandy for instance) and hand them out, then start transferring counts to the existing dukes regardless of de-jure status. In the end this will probably lead to civil war a long way down the line, but right now that isn't important.
You will soon either get the Saxon Wars event or an event which gives you a claim on another Catholic kingdom. That kingdom is almost always Lombardy, and winning the war is pretty easy. The only problem is that conquering Italy will bring you over the vassal limit again, which should be dealt with by further vassal transfers. The Saxon Wars though are much harder. To start with the event that triggers them tends to come at an inconvenient time, just after a major war for instance, and unlike Italy you can't put it off until later. The initial attack is relatively easy, just mass your armies and invade. You will need to set up forts as you go in order to deal with the pagan homeland attrition, which costs money, but actually fighting the battles isn't hard. For interesting events, try to capture as many Saxon nobles as you can, and also capture the temple holding of Paderborn.
The real difficult bit of the Saxon Wars is Widukind. After you win the Saxon Wars there's another event which also tends to fire at annoying times, which causes an uprising led by a Saxon warlord called Widukind. Widukind's army is much bigger than yours, usually around 12,000 men. Money is tight as Charlemagne and you'll need to pull out all the stops to hire mercenaries to deal with him: borrow from Jewish moneylenders, request money from the pope, ransom prisoners etc. With mercenaries you can just about top up your army to the same strength as Widukind, but victory is far from certain even with equal numbers. He's a very good leader with perhaps 25 martial, and you will be fighting in terrain that favours the defender. Fortunately Widukind is a rebel leader/adventurer and has no holdings of his own to reinforce from, so you can afford to whittle him down.
After Widukind there aren't many more events. There's the Iberian wars one, but that seems to be bugged. It does make sense to launch a holy war against Andalusia though, in order to secure the border duchies of Aragon, Navarra and Catalonia and prevent the fall of Asturias. Another fruit waiting to be plucked is Bavaria. You have two cousins who both have claims on the Bavarian throne, and you can use subterfuge to conquer Bavaria for yourself. First you should press one of your cousin's claims. Once the war is won, Bavaria will be ruled by a weak and hated Carolingian liege. Everyone in the realm will want him dead, so it won't be hard to assassinate him before he has children. Then assassinate the other cousin as well when he takes the throne, so that you inherit.
A word of warning for those who create the Holy Roman Empire: only kingdoms ruled by you will be incorporated as de-jure parts of the Holy Roman Empire. If you rule West Francia, Middle Francia and Italy, then the other kingdoms that you control but haven't actually created will be left out, for instance Burgundy, Aquitaine and Frisia. For this reason it's advisable to create as many kingdom-tier titles as you can, and also to conquer Brittany. You can also create the Empire of Francia instead of the Holy Roman Empire, which is arguably better since it's easier than gathering every kingdom in western Europe and it allows you to vassalise the Bretons easily. If you have Francia and then create the HRE later, Francia will be destroyed and replaced with the HRE.