an agreement by two or more persons to accomplish a criminal act or to use unlawful means to accomplish a non-criminal objective... husbands and wives cannot claim immunity. States differ on whether an overt act is required in furtherance of the parties agreement, which may be merely a part of the preliminary arrangements.
Actus rea is the unlawful agreement, and need not be formal or written.
Participants not even know or see one another as long as they otherwise participate in common deeds. The essence of the offense is the mutual agreement, not the acts done to accomplish its objective. The agreement need not be explicit, indeed often the agreement is implied from the acts of the parties and circumstances surrounding their activities. Also, all conspirators do not have to join the conspiracy at the same time.
In general, the prosecution must prove that a defendant intended to further the unlawful object of the conspiracy, and such intent must exist in the minds of at least two of the parties.