How shooting kills
Shooting can be carried out by a single executioner who fires from short range at the back of the head or neck as is the case in China. The intention of shooting at short range is to destroy the vital centers of the medulla (lower brain stem), as happens when a captive bolt is used for slaughtering cattle.
The traditional firing squad is made up of three to six shooters per prisoner who stand or kneel opposite the condemned who is usually tied to a chair or to a stake. Normally the shooters aim at the chest, since this is easier to hit than the head. A firing squad aiming at the head produces the same type of wounds as those produced by a single bullet, but bullets fired at the chest rupture the heart, large blood vessels, and lungs so that the condemned person dies of hemorrhage and shock. It was not unusual in earlier times for the officer in charge of the firing squad to have to give the prisoner a "coup de grace" - a pistol shot to the head to finish them off after the initial volley failed to kill them.

A bullet produces a cavity which has a volume many times that of the bullet. Cavitation is caused by the heat dissipated when the impact of the bullet boils the water and volatile fats in the tissue which it strikes. According to Dr. Le Garde, in his book "Gunshot Injuries", it is proved both in theory and by experimentation, that cavitation is caused by the transfer of the momentum from the fast moving bullet to the tissue which is mostly comprised of incompressible liquid.
Persons hit by bullets feel as if they have been punched - pain comes later if the victim survives long enough to feel it.
When all goes well shooting can provide a quick death but there are many recorded instances of it failing to kill the condemned person immediately. There are also instances of people surviving their execution. It would seem that one of the problems of the firing squad is that it is, typically, composed of volunteers rather than professional executioners and it is a task that many people would not find easy to perform when the time comes to actually squeeze the trigger.

Authorized Methods of Execution by State
AlabamaEffective 7/1/02, lethal injection will be administered unless the inmate requests electrocution.
ArizonaAuthorizes lethal injection for persons sentenced after 11/15/92; those sentenced before that date may select lethal injection or lethal gas.
ArkansasAuthorizes lethal injection for persons committing a capital offense after 7/4/83; those who committed the offense before that date may select lethal injection or electrocution.

CaliforniaProvides that lethal injection be administered unless the inmate requests lethal gas.
ColoradoLethal injection is the sole method.
ConnecticutLethal injection is the sole method.
DelawareLethal Injection is the sole method. Hanging was an alternative for those whose offense occurred prior to 6/13/86, but as of July 2003 no inmates on death row were elligible to choose this alternative and Delaware dismantled its gallows.
FloridaAllows prisoners to choose between lethal injection and electrocution
GeorgiaLethal injection is the sole method. (On October 5, 2001, the Georgia Supreme Court held that the electric chair was cruel and unusual punishment and struck down the state's use of the method)

IdahoAuthorizes firing squad only if lethal injection is "impractical".
IllinoisLethal injection is the state's method. However, it authorizes electrocution if lethal injection is ever held to be unconstitutional.
IndianaLethal injection is the sole method.
KansasLethal injection is the sole method.
KentuckyAuthorizes lethal injection for those convicted after March 31, 1998; those who committed the offense before that date may select lethal injection or electrocution
LouisianaLethal injection is the sole method.
MarylandAuthorizes lethal injection for those whose capital offenses occurred on or after 3/25/94; those who committed the offense before that date may select lethal injection or lethal gas.
MississippiLethal injection is the sole method.
MissouriAuthorizes lethal injection or lethal gas; the statute leaves unclear who decides what method to use, the inmate or the Director of the Missouri Department of Corrections.

MontanaLethal injection is the sole method.
NebraskaElectrocution is the sole method.
NevadaLethal injection is the sole method.
New HampshireAuthorizes hanging only if lethal injection cannot be given.
New JerseyLethal injection is the sole method.
New MexicoLethal injection is the sole method.
New YorkLethal injection is the sole method.
North CarolinaLethal injection is the sole method.
OhioLethal injection is the sole method.
OklahomaAuthorizes electrocution if lethal injection is ever held to be unconstitutional and firing squad if both lethal injection and electrocution are held unconstitutional.

OregonLethal injection is the sole method.
PennsylvaniaLethal injection is the sole method.
South CarolinaAllows prisoners to choose between lethal injection and electrocution
South DakotaLethal injection is the sole method.
TennesseeAuthorizes lethal injection for those sentenced after Jan. 1, 1999; others choose between the electric chair and lethal injection.
TexasLethal injection is the sole method.
UtahAllows prisoners to choose between lethal injection and firing squad.
VirginiaAllows prisoners to choose between lethal injection and electrocution
WashingtonProvides that lethal injection be administered unless the inmate requests hanging.
WyomingAuthorizes lethal gas if lethal injection is ever held to be unconstitutional.
U.S. MilitaryLethal injection is the sole method
U.S. GovernmentThe method of execution of Federal prisoners for offenses under the Violent Crime Control and Law Enforcement Act of 1994 is that of the state in which the conviction took place, pursuant to 18 USC 3596. If the state has no death penalty, the judge may chose the method of another state. For offenses under the 1988 Drug Kingpin Law, the method of executions is lethal injection, pursuant to 28 CFR, Part 26.
(Source: Bureau of Justice Statistics, Capital Punishment 1996 Bulletin, Table 2 (Dec. 1997); updated by DPIC)