Caesium is an alkali metal. The two important factors to remember for this idea are that caesium reacts violently with water, and that caesium spontaneously catches fire in the air.
A Caesium Gun would use these two factors as a means of causing harm and a propellant.
In a cartridge, an amount of water and caesium, tightly packed, would be held apart by a disc. At the end where the caesium would come out is another disc, or perhaps a flimsy material that the caesium would punch through upon reacting with the water. Perhaps there could even be a metal tip on the end of the caesium, to add to the bullet's penetration
Upon pulling a trigger or some other similar means of firing, the disc would be knocked out of place, allowing the water to fill the area, reacting violently with the caesium. The violent reaction would hopefully propel the caesium out the end of the gun at a high speed, as it starts burning in mid-air. The heat and speed would, hopefully, allow it to cause a good deal of damage to whomever is on the wrong end of the gun. Furthermore, if it were to go inside a human, or most any creature you would be firing it at, it might cause a sizable explosion, due to the great deal of water that sits inside a lot of living things. The physical and psychological effects of such a thing would be sizable.
The bullets would be difficult to produce, and it might be even harder to make sure the caesium doesn't react with anything before you have an opportunity to use it. However, given the right circumstance it could be a spectacular weapon.