Being a Civ player, I imagine you can manage the land battle part, so I'll address the other aspects.
Some cities/nationalities may be on too good of terms to offer you the attack option. You can judge the port's hostility by how rapidly their flag flaps. More flaps, more hostility. You can antagonize them by engaging ships outside the port and by using your space bar to bombard them.
The number of pentagons on the coastal fortress is an indication of strength. The fewer, the weaker.
You can soften up cities for capture by cooperating with natives and pirates, and letting them attack first.
When you fight a land battle you want to defeat all of the enemy companies of men, not just make it to the city gates. When you win the first time, you can recruit more crew to replenish your losses in the tavern.
When you march out of town you can turn around and attack again. You may have to attack 3 or 4 times to capture a city. It's not about luck, it's about depleting the garrison.
If you get the garrison down to about 60 and attack ( it may depend on difficulty level ) you will fence the captain of the guard instead of a land battle. If you win that one you will capture the city.
So bring lots of men, get lots of help, and attack, attack, attack.
Any questions?