Guns were widely used during the time of the American revolution. Connor can of course use them as well. As for ranged weapons, his basic equipment includes a pistol and an Indian bow, but you can also use muskets left by soldiers.
In order to use one of the above weapons, you need to hold down and let go of the proper button. It's a basic method which works well with nearby targets.
Where higher precision is needed, you need to hold down the aim button before shooting and move the dot to the proper position with the right analog stick.