The red team's objectives and duties include:

Compromising the target's security via obtaining information, penetrating their systems, or breaking their physical perimeters.
Avoiding the blue team's detection. Many attacks happen in a split second, making it difficult for the blue side to neutralize the threat before the 'damage' is done.
Taking use of flaws and faults in the target's infrastructure. This identifies technological security weaknesses that must be addressed in order to improve the organization's security posture.
Initiating hostile action, such as advanced penetration testing, to provide a reliable assessment of the blue team's defensive capabilities.

The methods used by the red team include:

Initial reconnaissance - gathering information about the target using open-source intelligence (OSINT).
Establishing communication with the target's network by deploying command-and-control servers (C&C or C2).
Using decoys to keep the blue team guessing.
Using social engineering and phishing techniques to persuade employees to give or expose information in order to breach their computers.
Cloning an administrator's access cards to obtain access to regions that aren't prohibited
Penetration testing, both physical and digital - usually done in a vacuum.