I've been playing a bit of Napoleon Total War lately, and out of all of the games in the series, I think it is my favorite, if not a close second to Empire (since Napoleon is an improvement on Empire, its hard to say). I've also decided to do a few mini-guides to the campaign maps, just for fun. Since I'm assuming you can get through the tutorial okay (if not, you have bigger problems), I will start with the Italian campaign.
Beginnings: In the beginning, you have a few small armies, a couple cities, and the little mastermind himself. You should take Napoleon and his army and deal with the nearby Austrian army (its a simple battle, especially with Napoleon. Think of it as a warmup). You should take your other army (on the left) and siege Coni. When sieging it is always worth waiting to be counterattacked by the defenders as defending is easier than a direct attack (unless you have a good reason to need that city today). The siege of Coni is easily won with the army you have. Set up your artillery on the left, where there is a good hill (always look for a good hill for your artillery). When defending, you should make your infantry into wedges (think inverse triangle) so that two units cover the same field of fire, creating a crossfire. Defensively, this will chew up the enemy when they charge.
Once you capture the city, you should build a supply post in the town of Mondovi. Supply posts are vital for the continued advancement of your army as it allows rapid replenishment of wounded units. You should develop buildings as soon as possible, as there are so few. Improving buildings are roads are important for the long-term viability of your empire.
Occupation: With Napoleon Total War comes new occupy options for captured cities. It is almost always in your best interests during the campaign to peacefully occupy cities to avoid unrest. This campaign is ultimately a speed game, so you cannot afford to waste time and units occupying a city, and any time it is in unrest hurts you. Your mileage may vary.
Battle of Turin: Combine Napoleon's army and any healthy survivors from Coni, and advance towards Turin. As mentioned, lay siege and wait for a counterattack. The siege map has another excellent hill for your artillery. Be sure to watch your flanks in this map, as it can be easy to get outflanked (splitting your army into two sides, one for each flank, can help but isn't completely necessary if you pay attention). With the capture of Turin, you should build any available buildings, and reinforce if possible. Let your troops rest if possible, you will need them soon.
There is a good chance that Piedmont-Sardinia will sue for peace and you should make them a protectorate. If they do not surrender. advance on Nuara, but they will be hurting after the losses you have inflicted. You should take full advantage of the protectorate status, set up trade routes and try to get them to join you in your war with Austria. Either way, build up your armies for the next battles.
Milan and Lodi: Now its time for the tough battle: Milan. Build up your army and head through Piedmont-Sardinia and to Milan. Milan's battlefield is a horribly flat piece of land infested with Austrians. Flat is not ideal for the artillery-loving Napoleon, but it will have to do. The battle will be tough, but if you have brought enough reinforcements, and you destroy the enemy instead of letting them retreat to face them another day, you will succeed.
After Milan is taken care of (and your troops are ready), take Lodi for your trouble. Austria can be fickle about defending it, and sometimes they will send a lot of troops, but more often it is left with a small force. As always, build up any buildings you can, solidify your army and prepare for the next phase.
Mantua and Parma: You've probably been given a mission for Mantua by now. This will require you to split your army, and you should make two armies with good mixes of units. To make things worse, the Papal States are waiting to join the fun, on the enemy's side. Take the army that is not led by Napoleon to siege Parma, which should be a fairly straight-forward battle. You should take your army led by Napoleon and take him north to take Mantua. This will be a very tough fight, and you will be counterattacked, so ensure if you have any extra units to add them to this army. Napoleon will have to hold his own for a little while.
Modena: Now, advance with your second army and take Modena. Modena is one of the few cities that you can siege without much reprisal, and its in your best interests to wait. The Papal states have a trigger that fires when Modena is taken, and they will declare war on you. It can happen before, but why rush things when you can have a couple of turns to rebuild and reinforce? You will need those reinforcements, because you are fighting against three foes: Venice, The Papal States, and Austria. Modena will be a stronghold against the Papal States, so fight defensively there (use trenches if possible, Napoleon Total War means death to armies that use buildings to hide in).
On to Venice: Once the Papal States are engaged with you in war, Napoleon should strive to eliminate one of his enemies. You should march as swiftly as possible to Verona. Once Verona is taken, leave some troops to defend it (or move some up from other cities) and push on swiftly to Padua. Verona will be attacked, so play smart and try not to loose the city. Once Padua falls march on to Venice itself. The fall of Venice means the fall of the Venetians. Reinforce Napoleon's army, and head for Trient.
The Papal States: Since Austria is a big monster, the next target in the unholy trinity is the Papal States. The first target should be Bologna (with your second army, Napoleon is heading for Austria). Once that is taken, take Ancona. If you keep up your momentum, minimum garrisons are fine for cities you take, you have your enemy on the defensive and they do not have units to spare to retake these cities. With the fall of Ancona, the Papal States are dead, and all that is left is Austria. Move all available forces to the area around Klagenfurt for the final fight.
Klagenfurt: The Mountains near Trient will be bristling with Austrians. Mountains, however, are good places for artillery emplacements, use them to your advantage. Be cautious and you will win these battles and route the filthy Austrian menace. Once Trient is taken, you should consolidate forces near Klagenfurt. You will need a sizable army for the battle, but it is the last battle of the campaign, so use all available resources. Once you take the city, the campaign is won.
Hope that helps