After you are arrested and taken to jail, you must appear before a judge and be told what charges you are being accused of and reminded of your right to an attorney and right to remain silent. What is this process called?

The process Is called Miranda warning.

Miranda warning is a preventive criminal procedure that states that law enforcement agencies are required to protect an individual in custody,who is subjected to direct questioning from the violation of the fifth amendment right against compelled self incrimination.

The Miranda warning goes thus;

You have the right to remain silent.Anything you say can be used against you in the court of law .You have the right to a lawyer during questioning,if you can't afford a lawyer,one will be appointed to you if you wish.If you wish to answer a question without a lawyer,you have the right to stop answering at anytime.

Explanation:

c. reserves power to the states and people