How the current method works

As Said before the current and most popular method of lawful execution is the Lethal Injection, this method is used in several states in the United States, of course other quick methods like hanging and lethal gas are used, the following picture shows what States use the following, keep in mind this is only for the United States of America.

The United States became the first country to use the lethal injection in the year 1982 Oklahoma became the first state to adopt a lethal injection legislation. of the 38 States that use Lethal injection, approximately 34 use it as a primary mean of execution, leaving the other methods behind.
As of 1994 this method became more adept to using the lethal injection, it increased from 27 to 37 on 2004.

Other countries began using the lethal injection method in 1997, China become a popular one for its many executions. Other countries like the Philippines, Guatemala and Taiwan also adopted This method around the same year. The current process used in China is most likely not similar, They keep their methods secret and it is hard to obtain any information at this current time.
To date Approximately 120 countries have a sort of Capital punishment, but 20 of these have not executed a convict in the last 10 years or more.

Usage of the Lethal Injecction

As the Bill of rights denies the cost ancient ways of execution, like the guillotine, the Electric chair, these Unusual and painful in our society. There "Lethal injection" is in reality 3 separate injections  that are administered to the convict to execute him. The first includes Sodium Thiopental, This numbs the killer unconscious, it is an anesthetic.The seconds is a Pancuronium, which causes full paralysis of the body. And the last contains Potassium chloride, which will cause a cardiac arrest while in the paralysis, Leading the killer to it's death.
As a fact, From the Time the first Injection is given, Death should be assured in a limit of seven minutes. Also a killer, after being given the second injection would die naturaly of asphyxiation. The following video Explains the Cons side of The usage of the Lethal injection.

Most of what is stated in this video is factual, The anesthetic is mostly not given properly, and it will cause torture. Since The Hippocratic Oath is in place, no doctors can be around to examine or distribute the shot properly. Most people would agree with this argument as it states that it tortures the killer in a inhumane way.

However the Point of the Lethal injection is the act of retaliation, to get back at the killer for the horrible did he did to one's friend or family member. Vengeance is a  common feeling for many people who lost a dear one thanks to a killer or to anyone in society, that family member most likely would like to do it himself, and in the same manner, but no one is allowed to execute justice on their own due to the current government. The fact that the killer is being tortured in the death bed is not only convenient and fair, but also satisfactory to any relative or friend of the victim(s) the killer murdered. as by our nature as humans we like to not only see violence,  but see those who damage  and hurt us suffer a same or worse fate. Various sources like pro and anti death penalty.org have varying opinions, Pro death penalty says there is a "low to none" chance of the anesthetic being distributed improperly, leading the inmate to a slow and painful death, but also that jail men and guards have training before starting anesthetic procedures.While the Anti death penalty website says that a degree is absolutely necessary for this, it does admit to jail men receiving training, therefore there is a common ground in the two sides but ones side like the cons website uses this as a way to what some might call it "demonise" the Lethal Injection.

Introduction to the Death Penatly

The Death Penalty is the capital punishment in the United States of America. The Capital Punishment is granted when the offender is declared guilty for any case involving murder. This is used as a way to honor the family or friends of the victim, the same method as the ancient "eye for an eye". When the method was first created it was executed with the Electric chair. now in modern America, the most common method it is to use the "Lethal Injection", this is due to the Bill of Rights saying that it is forbidden to give out cruel and unusual punishments.
Proponents of the Death penatly state that it is an essential tool to preserve our society.
Opponents of the Death penalty say its is a wrong method of punishment as it lets the government take human life's.