These are just a few of the ways to level feel free to add to the list as the system changes. Or comment on anything I missed.
Leadership (this ones pretty tough to level)
#1. Talk to everyone you see its possible to get XP from conversations.
#2 Complete Quests.
#3 Pay your crew when you're told to.
#4 *NEW* Find a damsel in distress and rescue her. (I got 10% from saving a girl from thugs in the jungle)
Melee
#1 Fight everyone you see.
#2 Fight everyone you see.
#3 Find more people and fight them too.
Sailing
#1 Fight a storm.
#2 Sailing around will level this up but not as quickly as storms.
Accuracy
#1 Shoot people.
Cannons
#1 Shoot at other ships (only gains on actual cannon hits)
Grappling
#1 Grapple onto other ships.
Repair
#1 Have your ship repaired
Defense
#1 Get hit.
Leadership (this ones pretty tough to level)
#1. Talk to everyone you see its possible to get XP from conversations.
#2 Complete Quests.
#3 Pay your crew when you're told to.
#4 *NEW* Find a damsel in distress and rescue her. (I got 10% from saving a girl from thugs in the jungle)
Melee
#1 Fight everyone you see.
#2 Fight everyone you see.
#3 Find more people and fight them too.
Sailing
#1 Fight a storm.
#2 Sailing around will level this up but not as quickly as storms.
Accuracy
#1 Shoot people.
Cannons
#1 Shoot at other ships (only gains on actual cannon hits)
Grappling
#1 Grapple onto other ships.
Repair
#1 Have your ship repaired
Defense
#1 Get hit.