Belgium begins the game as having strong industry, and one of the only railways in Continental Europe (just between Antwerp and Brussels). It's not much, but every little bit helps. The strategy you take will depend on what you want to maximise, your Military or Industry.
The following assumes that the reader is familiar with the basics of Victoria's play.
First of all, Don't Panic!
Belgium begins at war. There are two things you can do. The first is to ally with Britain, the second is to wait. Britain begins with a very high relationship score with Belgium, so you'll almost always be able to ally with them. The instant they say yes, they're into the war, and will usually do useful things like land a couple of divisions in Amsterdam, which will make the Dutch more inclined to accept Belgian independence.
Waiting is also good because eventually the Great Powers get together and sign the London Treaty, recognising Belgian independence. This always happens within six months of the game's start, and quicker if you've allied with England. If you are not allied with Britain, there's a small chance the Dutch won't accept the Treaty, and the war will go on - you just have to fight it out. If you are allied, then they should accept it, and will usually accept it even if you're not allied with Britain. At greater than normal difficulty level the Dutch are more inclined to fight on - in which case, the British will usually lend you expeditionary forces to fight with, as well as doing their own fighting. Save your money and lives, and let them do the fighting for you.
So it may be that you don't need to fight at all. On normal difficulty you begin with 8,000 pounds. I try to keep it, so I just slide Army, Navy and Defence down to zero and withdraw the army to Brussels, to await the London Treaty, and/or British help.
Once they accept your independence, you get peace, and Arlon added to your borders.
For this, you need manpower. Have a look at the RGO in each province, how much gets used. You'll find that there are a few cheap things like coal that are over-produced to begin with - you can turn some of those guys into Soldiers. The practical limit for Belgium in the first ten years is about ten or so divisions. After that, you collapse your economy and go bankrupt.
However, Belgium should not be fighting alone. England begins friendly, and Russia and the Turks are also friendly - but obviously with them you'll have to choose sides! Lots of German minors are friendly, too. In the case of war with Prussia or Austria, because they have treaties with them, they'll usually not fight for you - but at least if you're allied they won't fight against you, either.
An alliance secured, you should be able to have a little conquer-fest. Essentially you have to choose whether you're going east to Prussia/Austria, or west to France, and stick to that direction for the whole game. This is because you can only go one way if you ally with the guy on the other side; if you don't, you get squashed between them.
Try to focus on cavalry and dragoon units with lots of artillery, to rush ahead and snatch provinces. Let the French or English or Prussians do the bulk of the fighting and dying for you.
The other method of securing manpower is by building colonies. The Africans and Asians will almost never come to Europe's factories - but you can stick them in your divisions.
Once you've secured new provinces, you'll be able to divert more manpower into the military.
To maximise industry, forget about colonies. Colonies provide raw materials. If you build the colony yourself, you're looking at an outlay of 20,000 pounds or more, once you build settlements in each province and then claim it. Of course, you can snatch the colonies off someone else, but then you have the expense of a war, instead. If you're going to have the expense of a war and santch provinces, why not do it in Europe?
For example, Belgium has a war with the Netherlands and takes Maastricht in the peace settlement. You'll probably find that there are 20,000 Craftsmen and 15,000 Clerks cut off from their factories in the rest of the (Dutch-held) state. If you have vacancies in your factories in Vlaandern, they'll go there. And then you'll have boosted production.
To boost industry, convert everyone to Craftsmen and Clerks, leaving only a token 1 POP in each RGO in your country. Go through your factories and see what raw materials they need, and make sure you import those. Industrial rating is in factories, not in RGOs, and export money is in factories, too. Almost all finished products have a higher price than the raw materials. The only reason to seek to control colonies is if there's a shortage of some raw material you want. For example you may wish to make Luxury Furniture, and find there's no Tropical Wood about (or you've got low Prestige and can't get it!) So then it becomes worth getting a colony.
In general, though, you shouldn't need them. The factory goods most in demand for the first half of the Grand Campaign are Regular Clothing and Glass. Belgium begins with a Fabric Factory, and Coal Mine RGOs, so you just need to import Dye and convert your pops to Craftsmen/Clerks. Furniture is also a good one, but you'll need to have a Lumber Mill first, as there tends to be not much Lumber on the world market, but plenty of timber. You can usually get the technology/inventions allowing Machine Parts Factory by 1848 at the latest, but you probably won't be able to afford to build it.
If you don't feel it's an exploit, you can use your good relationship with the Turks to buy Greek provinces off them in exchange for technologies. Convert these Greeks to Craftsmen/Clerks, and within a year or two they'll have all migrated to Belgium - extra manpower for your factories. Then you can give the provinces to someone for money - the British will always buy them.
One advantage of this approach is that you can then afford to lose wars later on, giving up those outlying provinces to the invaders. Once you have their manpower for your factories, you don't care about the nearly-empty provinces.
Events over the Grand Campaign
Few international events directly affect Belgium after its foundation. You have to choose to get involved. If, for example, you're hoping for opportunities to annex parts of West Prussia, the thing to do is to develop your relationship with Denmark, then allying with her. Denmark has a very good chance of ending up at war with Austria and/or Prussia about 1848 and 1862. If you're still allied with France or England, France will take care of Austria for you, and rush through West Prussia and any minor allies of Prussia, while you can grab a few provinces from there. It's likely Britain will land on the Baltic coast of Prussia and march on Berlin. Once the Union Jack's flying over the Reichstag, the Prussians get generous with their provinces.
I consider it a good long-term strategy for Belgium to get involved in the wars in Germany, because a united Germany - whoever the master is - means a squashed Belgium. Belgium is one of the highways of Europe, you don't want smelly Germans and Frenchman stomping about your lovely country, do you?
Other events are the European Intervention in Mexico, and the Crimean War. If you're allied with Britain or France, they'll probably invite you to the Mexican adventures. There, you can grab territory, or march on the capital, and then make a separate peace for indemnities, which is a good source of cash for you. They won't invite you to the Crimean War, but if you're allied with the Turk, he definitely will. Russia is so huge and your army so small in comparison to theirs that you won't be able to do much there, unless you are very bold or crazy and land at Revel and march on St Petersburg! Doable in normal difficulty games.
In general, if you are allied with the French or the Turks you will end up in heaps of wars, and have lots of opportunities to gain or lose territory. The Russians and English don't invite you to join in their wars very often.
Last of all, Don't Panic!
Players used to playing the Great Powers will often end up bankrupting a minor power very quickly. A minor power must pay more attention to diplomacy than a Great Power, and make good use of the "Open Negotiations" button. Take things slowly. Choose your technologies you're researching carefully. For example, suppose that in 1838 you have the chance to research Iron Railroad. Don't bother. You won't be able to afford to lay the tracks anyway! Research something else instead, depending on whether you're aiming to maximise industry or the military. Be patient, and don't panic.
It's not really possible, as Belgium, to end up #1 in all three areas without going for all-out conquest and racking up lots of BadBoy points (the only exception would be with some very well-chosen Colonial Wars, snatching claims, and trading very carefully to build up a colonial empire). But you can certainly become #2 or #3 in Industry, and pretty high in Prestige, too. Being the 5th-ranked Great Power by about 1865-70 is not difficult if... you don't panic, and stay patient.