Well, first you take a bottle of lube, then you bend over, and then...
Seriously, though, I'm not quite sure where to start. Not only does the game have a ton of systems and mechanics, they are also interconnected to the point that it's hard to explain one without explaining something else first. But here goes a few tips:
1. Pick a European nation. Specifically, a nation with the Western European tech group. There is pretty much no reason not to do so. A solid pick when learning the game is Spain, since they are basically the game's easy mode - good starting position, no real opposition, can easily colonize, dominate trade, conquer the Old World, etc.
2. Monarch points are the lifeblood of the game. You need Admin, Diplomacy and Military points for pretty much anything, but most importantly you need them for Technology and Ideas. Don't waste them and take pretty much any chance to get more of them. Also, try to keep some in reserve for emergencies. Gold is nearly worthless past the early game, it's just so easy to make more of it. Advisors are helpful here, as they generate more points for you (and provide specific bonuses), but be careful as they can be a bit on the expensive side.
3. Trade is the easiest way to make money, but it can be a bit hard to understand. Basically, every province in game belongs to a
trade node and contributes trade income based on its production to that node. Any country with a province in a node can have
Trade Power in that node. More provinces = more power. More trade ships in that node = more power. Power determines the "cut" of the trade income a country has access to. Any country with a capital city in a node will cash in on the income (based on how much trade power it has there) and the rest will get forwarded to nodes further down the line (represented by the arrows in the trade view) and amplified. So, longer trade lines with no cashing out means more money.
Merchants can be used to alter the flow - either by cashing in or by forwarding the flow of money in a certain direction. Trade ships can be used to increase your power in a node, and together with merchants help you determine where the money flows. If you hold an overwhelming majority of Trade Power in a node, you can just send all the money to where it helps you the most.
For instance, as Spain, you could set up colonies in the New World, dominate a few key trade nodes and force any money that passes through them to go to your home node. Or you could colonize along the African coast, link up with the rich trade in India and China, then overwhelm them with Trade ships to the point where you pretty much take all their trade and send it "downriver" towards Europe. With each jump it gets amplified and picks up more cash from each node, resulting in a snowball effect. If you set it up right, by the time it reaches Spain, it'll be a massive amount.
4. Mind your expansion. It's easy to get carried away and conquer waaaay too much, causing everyone to hate you and for coalitions against you. Pace yourself, let things cool off for a few years after conquering stuff. Consider forcing smaller nations that you defeat to become your vassals instead of outright annexing all their stuff. This causes less bitching from your neighbors and you can start to annex them diplomatically after a few years. Any new provinces you do annex will add to your Overextension (you do NOT want this number to get above 100%, EVER!) and need to be "Cored", which tends to cost Admin points and take time. One way around this is to give the newly conquered provinces to a vassal of yours or to create a new vassal out of those provinces - when you later annex them diplomatically, you'll get cores automatically.
5. Keep up in tech, but don't go overboard. If you tech too fast you'll notice that the cost of tech starts to get pretty high due to the "Ahead of time" penalty. A 10-20% penalty is OK, but more than that is just a waste, unless you are capped in that particular category of points.
6. Be smart about your idea choices. You need Colonization as your first or second idea if you want to do any serious work in that regard, and you pretty much need to rush those ideas because early colonization is a land grab. Religious is a great idea group in general and I suggest you keep it in mind. Most military idea groups are solid, but you don't need too many.
7. Keep an eye on your Diplomatic relations number - if you go over the limit it'll lower your Diplomatic point income. Each relation represents a country with which you have active treaties - that's the important part, it counts COUNTRIES, not the treaties themselves. So, if you have Royal Marriages with three countries, this means three Diplomatic relations, but a Royal Marriage, an Alliance and Guaranteeing Independence with a single country is only one relation, even though it's three different treaties. One thing worth noting - if a country is giving you Military Access, that counts as a relation, but if you are giving THEM access, then it doesn't (at least not for you).
8. Stability is another really important number. You don't want this to go negative - if it does, spend Admin points to get it back up. DON'T spend points if it's at 1 or more, as the price goes up dramatically and it's not really worth it.
9. Legitimacy and Prestige are less important for the most part. Just make sure you Prestige doesn't go negative and your Legitimacy doesn't get too low (say, under 30) and you should be fine.
10. A nice early game trick is to drop your military upkeep down to zero - this saves you a ton of money, but your troops will fight like shit due to low morale. You can get it back up if war seems likely, though it'll take some time for morale to recover.
11. Don't go overboard with constructing upgrades in provinces. The monetary cost is irrelevant, but the Monarch point costs add up. 10 points isn't much, but if we're talking about 100 provinces (a fairly reasonable proposition), that's a tech level or two right there. In general, spending monarch points to make more money isn't a good idea. Manufactories are an exception, as they potentially let you monopolize the market on certain goods and get passive bonuses out of it. Also the Gold/MP ratio on them is decent so they do make a reasonable investment. Military buildings can also be worth it as they can provide Manpower and Forcelimit bonuses to smaller countries that would otherwise be starved for it. Unique buildings are great and should all be built.
12. Army composition depends on the culture you are playing, but as Europeans, you'll mostly be infantry based, with a bit of Cavalry splashed in. You should be looking at Infantry/Cavalry/Artillery ratios such as 5/1/1, into 10/2/5 midgame, shifting into 10/5/10 later in the game. The reasoning here is that European cavalry sucks balls during the first half of the game so you only bring a little for flanking. Early artillery isn't too stellar and you mostly want it for siege bonuses. However, as tech advances you get new Cavalry types that aren't garbage and artillery bonuses start to add up, meaning you can put more of them into your armies. The combat model is actually quite detailed "under the hood", and a lot of things factor into it, so combat can seem a bit random or opaque, but there is method to the madness.
Alright, this is all I can think of at first glance. If you have any questions, go for it
