The Cannoneer's Combine ability acts very similar to the Chemist's Mix ability.
When you are in a battle, select the "Combine" action. This will bring up your item screen. You need to first select a type of shot. There are three types to choose from: Buckshot, Blitzshot, and Blastshot. There is only a difference between the three, when you are damaging enemies with them, otherwise the effects of the shots seem to be the same.
Once you have the shot selected, you then choose the item you want to combine it with. Then the attack will commence.
The items you choose have different outcomes to them. Below is a table showing the shots, items, and what the outcome will be.

Item	Blastshot	Blitzshot	Buckshot	Description
Dark Matter	Chaos Burst	Chaos Cannon	Chaos Shot	75% chance of casting Poison, Death, or paralysis
Ash	Dark Burst	Dark Cannon	Dark Shot	75% chance of causing Blindness
Hero Cocktail	Divine Burst	Divine Cannon	Divine Shot	Attacks with Holy power
Dragon Fang	Dragon Burst	Dragon Cannon	Dragon Shot	Critical damage to dragons
Flame Scroll	Flame Burst	Flame Cannon	Flame Shot	Attacks with power of fire
Fuma Shuriken	Killer Burst	Killer Cannon	Killer Shot	Critical damage to huminoids
Mallet	Mini Burst	Mini Cannon	Mini Shot	75% chance of casting Mini
Gold Needle	Needle Burst	Needle Cannon	Needle Shot	Causes 1, 2, or 3,000 dmg to target
Shuriken
Power Drink	Power Burst	Power Cannon	Power Shot	75% chance of casting Berserk
Goliath Tonic	Quake Burst	Quake Cannon	Quake Shot	Attack with power of Earth
Speed Shake	Silver Burst	Silver Cannon	Silver Shot	75% chance of casting Old
Turtle Shell	Slow Burst	Slow Cannon	Slow Shot	75% chance of casting Slow
Lightning Scroll	Spark Burst	Spark Cannon	Spark Shot	Attack with power of Lightning
Iron Draft	Vulner Burst	Vulner Cannon	Vulner Shot	Drops targets defense 75%
Water Scroll	Water Burst	Water Cannon	Water Shot	Attack with power of Water