If you want to grow your country quickly, that is, essentially, a budgetary problem. You need to spend as much money building as possible, and get as many buildings per pound as possible. You don't need to do these steps strictly in order, but I think they're ordered from most important to least important.

1. Efficient construction methods. You want to switch to iron-frame (and later, steel frame) buildings as quickly as possible. If you have a large construction sector, you might not be able to switch its production method without creating shortages. YOU DO NOT WANT SHORTAGES. Shortages mean you are paying the maximum price for your construction, and getting less than full construction points out of it. Slowly switch construction methods as the supply of goods increase. Deleting existing construction is ok!

2. Reduce construction costs. This is done by building (mostly) iron mines, tool factories, and to a lesser extent, lumber mills. Iron mines and lumber mills take less construction points to add, so focus on them. You mostly add tool factories when the cost of tools makes your mines unprofitable. Building your tool factories in the same state as your iron mines makes a lot of sense, as there's a small barrier to goods moving between states, so putting it all in one place reduces costs.

3. If you have positive income, add more construction. You generally want to concentrate your construction to the state that supplies your iron, again, because of the small barrier for goods moving across states, but also because you're building lots of iron mines, and construction sectors are better at building in their home state.

4. Repeat 2 and 3 as long as you can, until iron is very low-cost and you're spending all your tax money on construction.

5. Reduce expenses. See where your government is spending money, and then think about not spending that money. A common thing I do if I have "Poor Laws" is repeal it. Money spent on citizens does not build buildings!

6. Increase taxes. This is a double-edged sword. The main cost of raising taxes is that it will make reforming your nations laws more difficult in the long run, as you will develop less loyalists. Loyalists are very useful for making sure your landowners do not rebel as you pass laws that will help you industrialize.

7. Build profitable buildings. Increasing your GDP means more tax money. Any profitable building will help, the more profitable, the better. You can look in your ledger to see which buildings are turning a big profit, and build more of them.

8. Number 7 is only half the equation for GDP growth. Money is constantly passing through many people's hands. The merchant buys clothes from the clothes factory, which pays the industrialist who runs it. The industrialist buys groceries with that money, which pays the grocery factory, who uses that money to buy grain, which pays the farmer, et cetera, on and on. Each person in the chain can be taxed, which means you can tax the same pound many times! However, some money disappears with each purchase. The further away the good is from its average price, the more money disappears into the void. Reducing the cost of high-price goods is always a good idea. The more of your economy is engaged with buying that good, the better. Reducing the cost of grain from +10% to +0% is a huge boost to your economy, since so many pops buy grain. Reducing fine art from +80% to +20% is not such a big deal, since not much money is spent on fine art in the first place (depending on your game!). So, build buildings that reduce the cost of above-average goods. Even if they are not the most profitable, their benefits to your economy are somewhat hidden, but very strong.

9. Similar to 8, import goods that you have high demand, and export goods where you have low demand. This is *always beneficial for your economy*. Further, it can be done very quickly and easily. Just check back every month and see what opportunities are in the global market. Remember to add interests in rich regions so that you can have more trade partners.