The objective of Vasa Regalis is two-fold: acquire as much goods as possible and then place as little as needed on the ship. Let's look at them one by one.
The acquisition of goods
The goods are acquired and upgraded through the roles procurement (acquire) and craftsman/tailor/blacksmith (upgrade), all of which assure the player in turn at least 1 good more than the other players. Why at least? Because some actions deny the last player in the turn an action. This will guaranteed put the player in turn in a relatively better position than the other players. But there are ways to make this relative advantage even greater. If a player is unable to take an action (because there are no tiles left for that action), the distance to that player will be increased. Unless you don't need a specific good, you should always aim for the roles that give the other players as few actions as possible.
How about the Admiral and the King roles then? Well, they do give you a relative advantage of 1 good compared to all other players but no more. Thus, you should avoid those roles or, to be more specific, avoid putting yourself in situations where you have to choose those roles.
This leads us to another tactical trick: forcing other players to take those roles. If you have a good of value 3 and know that several players are stuck with value 1, it's usually good to build to force them to first play their low goods and then choose the Admiral role to replace them afterwards.
The King role may seem to be less valuable but in some cases, the King has a "take that" trick up his sleeves. If you know that several players have upgraded quickly to value 3 of a good but lack value 2, a build followed by the King role to force them to replace (to value 1) will put them in a difficult position.
The placement of goods
The goods are then placed on the ship but how much should you place? On average, all players must place goods of value 2 except one who places goods of value 3. If less, you want to be the player placing the 3 and if more, you want to be the player placing 1.
Generally, placing goods of value 1 is very risky since this would require at least 2 players to place goods of value 3 to prevent the ship from sinking (and you from losing). On the other hand, you need to take risks to win. Remember carefully which roles the other players choose and draw conclusions about what they have on their hands and how much they place on the ships. Players that upgraded quickly and then immediately built probably put a good of value 3 on a part. Players who look at your good on a part and then replace their own good are probably placing something differently than you (a low value good if you have a high value and vice versa).
The outcome of the first part may also affect the placement. Players who have acquired a lot of goods are less likely to take risks by placing goods of low value. If you are one of them, you could consider placing goods of value 2 to keep the part floating while still keeping a competitive hand. If you are not one of them, you could consider placing goods of value 1 to keep as much as possible at your hand.
In conclusion, maximize your relative advantage in the first part of the game and memorize all roles so that you can place just as much as you need on the ship afterwards.