Note: Certain upgrades will require you to reach certain points in the main story, and other upgrades you'll need to complete side missions or go treasure hunting to obtain the plans for.
You can upgrade the Jackdaw from the Captain's Quarters on the ship whenever the ship is docked.
Enter the Cabin
Select Outfit Ship
You can also purchase upgrades for the ship from Harbormasters, which you can find on your map with this icon: