Islamic rules of slaughter are intended to prevent torture of animals to ensure killing in the most humane manner as possible. The Prophet spelled it out clearly when he said:
"Allah enjoins compassion/ benevolence in everything; so when you kill an animal (for food) inflict the least amount of pain. So, make sure to sharpen the knife and bring comfort to the animal" (Reported by Muslim on the authority of Shaddad b. Aws)
Islam also forbids the killing of animals except for food; hence his specific orders to the soldiers going to war not to kill animals except for food.
While killing, we ought to kill the animals as humanely as possible: i.e. by inflicting the minimum of pain.
Now coming to hunting: We are allowed to hunt only for consuming the meat. In other words, Islam does not permit hunting as a sport or simply a fun, not for consumption.
As for hunting for food, we are allowed to do so using trained dogs or falcons, etc. we can also do us using spears and lances, as well as guns.
The Prophet said: "If you were to hunt using Mi’radh (an arrow which is slender at the two ends, and thick in the middle), and it hits the target by its sharp end, piercing the flesh (causing bleeding), then you may eat it. If, however, it has been hit by its thick middle part, then you shouldn’t eat it.” (Reported by Bukhari and Muslim on the authority of Adiyy b. Hatim).
In another tradition, one of his companions asked him about hunting with slingshots, and he replied, “They are not fit for hunting… for they (cause disfiguring and) breake the teeth and eyes.” (Reported by Bukhari and Muslim on the authortiy of Abd Allah b. Mughaffal).
In still another report the Prophet (peace be upon him) was asked about using slip shots: "You are allowed to eat what you slaughter by invoking the name of Allah (once it has fallen) bleeding.” (Reported by Imam Ahmad on the authority of Adiyy b. Hatim).
Based on the above traditions, eminent scholars have ruled: If a bird is shot down by guns, one should slaughter it if is caught alive; if however, the bird falls dead, you are allowed to eat it only if you fire the shots by invoking the name of Allah.
What we stated above is the preferred view of eminent scholars since guns used for hunting today are sharp; they pierce the flesh causing bleeding. Hence it is comparable to Mi’radh mentioned in the well-attested tradition cited above.