Conspiracy has been defined in the US as an agreement of two or more people to commit a crime, or to accomplish a legal end through illegal actions. For example, planning to rob a bank (an illegal act) in order to raise money for charity (a legal end) remains a criminal conspiracy because the parties agreed to use illegal means to accomplish the end goal. A conspiracy does not need to have been planned in secret in order to meet the definition of the crime. One legal dictionary, law.com, provides this useful example on the application of conspiracy law to an everyday sales transaction tainted by corruption. It shows how the law can handle both the criminal and the civil need for justice.
[A] scheme by a group of salesmen to sell used automobiles as new, could be prosecuted as a crime of fraud and conspiracy, and also allow a purchaser of an auto to sue for damages [in civil court] for the fraud and conspiracy.
Conspiracy law usually does not require proof of the specific intent by the defendants to injure any specific person in order to establish an illegal agreement. Instead, usually the law only requires the conspirators have agreed to engage in a certain illegal act. This is sometimes described as a "general intent" to violate the law.
In United States v. Shabani, 513 U.S. 10 (1994) the United States Supreme Court ruled: U.S. Congress intended to adopt the common law definition of conspiracy, which does not make the doing of any act other than the act of conspiring a condition of liability" at least in so far as to establish a violation of a narcotics conspiracy under . Therefore, the Government need not prove the commission of any overt acts in furtherance of those narcotics conspiracies prohibited by 21 U.S.C. § 846. The Shabani case illustrates that it is a matter of legislative prerogative whether to require an overt step, or not to require an overt step in any conspiracy statute. The court compares the need to prove an overt step to be criminally liable under the conspiracy provision of the Organized Crime Control Act of 1970, while there is no such requirement under 21 U.S.C. § 846.
The Supreme Court pointed out that common law did not require proof of an overt step, and the need to prove it for a federal conspiracy conviction requires Congress to specifically require proof of an overt step to accomplish the conspiracy. It is a legislative choice on a statute by statute basis.
The conspirators can be guilty even if they do not know the identity of the other members of the conspiracy. See United States v. Monroe, 73 F.3d 129 (7th Cir. 1995), aff'd., 124 F.3d 206 (7th Cir. 1997).
California criminal law is somewhat representative of other jurisdictions. A punishable conspiracy exists when at least two people form an agreement to commit a crime, and at least one of them does some act in furtherance to committing the crime. Each person is punishable in the same manner and to the same extent as is provided for the punishment of the crime itself. 
One example of this is The Han Twins Murder Conspiracy case, where one twin sister attempted to hire two youths to have her twin sister killed.
One important feature of a conspiracy charge is that it relieves prosecutors of the need to prove the particular roles of conspirators. If two persons plot to kill another (and this can be proven), and the victim is indeed killed as a result of the actions of either conspirator, it is not necessary to prove with specificity which of the conspirators actually pulled the trigger. (Otherwise, both conspirators could conceivably handle the gun—leaving two sets of fingerprints—and then demand acquittals for both, based on the fact that the prosecutor would be unable to prove beyond a reasonable doubt, which of the two conspirators was the triggerman). In order to achieve a conviction on charges of conspiracy, is sufficient to prove that a) the conspirators did indeed conspire to commit the crime, and b) the crime was committed by an individual involved in the conspiracy. Proof of which individual it was is usually not necessary.
It is also an option for prosecutors, when bringing conspiracy charges, to decline to indict all members of the conspiracy (though their existence may be mentioned in an indictment). Such unindicted co-conspirators are commonly found when the identities or whereabouts of members of a conspiracy are unknown; or when the prosecution is only concerned with a particular individual among the conspirators. This is common when the target of the indictment is an elected official or an organized crime leader; and the co-conspirators are persons of little or no public importance. More famously, President Richard Nixon was named as an unindicted co-conspirator by the Watergate special prosecutor, in an event leading up to his eventual resignation.