A couple of tips for new pirates:
Maximize your sailing and fencing skills (e.g., unless you are a “trader”, set your charisma to “1”). Sailing skills will help you close in on ships you wish to attack and help you elude ships that are more powerful than yours. Fencing skills will help you board other ships.
When you encounter other ships, compare their strengths and weaknesses against yours before deciding to attack or flee. In order to attack, you will need to outclass them in some attribute, be it cannons or manpower. If you outclass them in manpower, try boarding them. Boarding is usually the best option. If you outclass them in cannons and not manpower, use broadside attacks instead.
If you don’t outclass them, then you probably should try to flee the conflict (i.e., click on "Distance"). Add you sailing skills to your ship’s “rigging” rating and compare that to your opponent’s rigging rating. If you are the same or higher, then should be able to flee from them. If not, then you might give it a couple of quick tries anyway, but be prepared to fight. If you have a much lower rigging, then it is highly doubtful you will escape and you will be forced to fight you way out of it. This is the main reason it is risky to sail around with a rigging below "6".
When you capture a ship, consider seizing it (in other words swapping vessels) if it has better capabilities than yours. Once you get the hang of the game, a good tactic for getting wealthy (though a little risky) is to seize better vessels, sell them at the shipyard for a profit (by “buying” a lesser quality ship for a profit), and then going out and capturing a better quality ship, and repeating the process. One key to this is by to make sure your lesser quality ship has good rigging so you can pick and choose your battles (by outrunning ships you don’t want to fight). And when I say capture a better quality ship, you just need to have more men or more cannons so that you can win a battle via boarding or broadsiding respectively.
One last tip. Pirates go through lean times when their respective country is at peace with everyone. You can easily run out of food (and thereby risk a mutiny) if you don't have any enough cash on hand to keep buying food while you are "banned" from fighting. (And you aren't allowed to take it out of your retirement fund.) So saving your booty can save your booty.
Happy hunting!