EU4's management all falls into three categories:
- Administration
- Diplomacy
- Miltary
Each of these has it's own stock of mana/monarch points/power points. All of these categories has technologies and options for 'national ideas' (to help sculpt your playthrough).
Provinces has development in each category, representing it's amount of taxable farming, trade good production, and recruitable manpower. These get modified by the local autonomy, which shows how tight you're rule is. This can't go below 75% if the province is not part of a state...don't worry too much about this right now.
This covers making land part of your country ('core'ing it), taxation, and looking after colonies.
Cores:
- Coring initially costs 10 admin points
- Coring is the biggest expense in a big conquest campaign -- there's 20,000 devleopment on the map, but only about 75,000 admin points.
Taxes:
- Based off bae Tax and local autonomy.
- Money is the least useful resource, as all it can really be used for is making more money, and paying troops.
- That said, spending things other than money to avoid bankruptcy is worthwhile.
Colonies:
- Generally ignorable -- if you have money to make them, they won't be powerful enough to bother you.
- They're great for trade income and the like though, so always a good bet if you're in Western Europe.
- To get a Colonist, you will need to take 'Exploration' or 'Expansion' ideas.
Diplomacy covers relations with other nations, shipping, culture, and trade.
Culture:
- Your country has a primary culture, and possibly other accepted cultures.
- Provinces of your culture are easier to rule, make better money, and faster to 'core'.
Diplomacy:
- Vassals are a really good way to expand. You can release a country which does not exist but has a primary culture 'core' in one of your provinces. Then, you can use it's army, monarch points, and other cores to assit your expansion.
- Vassals that like you +190 can be integrated after 10 years. This costs 8 dip points per development, and gives you their cores (cheap that 10 adm).
- Rivals are a thing you can have. They help give you power projection. Someone who rivals you is your 'Enemy'.
- Allies keep you alive...except if they get attacked by someone more powerful.
- Allies are more likely to help you against their rivals.
- Ally France or the Ottomans if able.
Trade: A quick quide
- Gold is not a trade good.
- Trade value is generated base on the 'Goods Produced' in a province, multiplied by the value of the trade good in that province.
- Trade power is generated by provinces, merchants, and light ships
- In each node you have trade power, you could use that percentage of trade value.
- You automatically collect your percentage of trade value in your Capital trade node.
- In other tade nodes, you can send a merchant to collect or forward trade value.
- You can see the trade routes in the trade node map mode.
Trade: strategy
- Build up trade power in your capital trade node.
- Once this is high as you can make it easily, look at building up trade power in the nodes upstream from you, and transfering more value into your node.
- Colonial nations (americas) and trade companies (india, china) can give additional merchants.
Navies:
- Unless interacting with Britain or similar, in early strategies, focus on light ships that can help you with trade
- Once you have trade ships, you have to select them, and then tell them to go on missions to assign them to a trade node.
- Galleys are stronger than heavy ships in the Meditarian and off the Chinese coast.
Miltary is the most complex topic in many ways, and adds a load of additonal resources. If you want to understand combat in this game, I highly, hightly recommand Reman's series that goes over all of it: https://www.youtube.com/watch?v=O63oZQpKt_g
You have and army, made up of 1000 troop regiments. They have a Morale values, and various combat states. You can raise new armies or reenforce existing one using money and manpower. Manpower slowly regenerates based on the total Base Manpower of all your provinces, modified by autonomy.
How much your court things you have the right to rule. Affects unrest. Higher is better, but worth sacrificing for a lot of things -- 5 legitimacy will generally take 2-4 years to come back by itself.
A really important resource that makes your army fight better, and is easiest won in wars. However, there are a lot of events and options that will give you the option to spend it -- good if you know you can win it back.
Basically a measure of how much you've trounced your rivals recently. Although officially a 0-100 scale, the only relevant value is 50. This gives you one extra monarch point in all three categories per month.
First off, you can only get a max of 15 (this is a lie) of each monarch point a month. Ever 13 years, you will be looking to spend about 600 on technology, which uses a little under four of those per-month points.
In the early game, you are likely to be limited in terms of money, manpower, and monarch points. Of these, money is the least important -- barely making money but having an advisor generating an extra point or two is better.