(CNN) The college admissions scheme revealed Tuesday is the largest of its kind ever prosecuted, federal prosecutors said, and features 50 defendants across six states, millions of dollars in illegally funneled funds and a handful of the country's most selective universities.

But at its core, the alleged scheme is remarkably simple -- and brazen.

Cheat on standardized tests. Bribe the people who decide which students get admitted. All the while pretending that money was for charity.

"I'll speak more broadly, there were essentially two kinds of fraud that Singer was selling," US Attorney Andrew Lelling said, referring to William Rick Singer , the figure at the center of the scheme.

"One was to cheat on the SAT or ACT, and the other was to use his connections with Division I coaches and use bribes to get these parents' kids into school with fake athletic credentials," Lelling said at a press conference in Boston.

A total of 50 people were charged in the case. Those arrested include two SAT/ACT administrators, one exam proctor, nine coaches at elite schools, one college administrator and 33 parents, according to Lelling.

Here's how the plan worked, according to prosecutors.

Cheating on the ACTs and SATs

Of course, students who score higher on standardized tests such as the ACT and SAT are more likely to get into selective colleges.

Given that, Singer facilitated cheating on those exams for students whose wealthy parents paid for his services.

Singer pleaded guilty in court on Tuesday to four federal charges and admitted that the case against him was accurate.

According to the indictment, he arranged for a third-party -- generally Mark Riddell, who is charged with two conspiracy counts -- to secretly take the test in the students' place or replace their responses with his own.

How did Riddell allegedly take the tests without being noticed by the test administrators? Well, prosecutors said, Singer bribed them.

Igor Dvorskiy, who administered SAT and ACT tests in Los Angeles, and Lisa "Niki" Williams, who administered the tests at a public high school in Houston, are both accused of accepting bribes to allow Riddell to take the tests. Both are charged with conspiracy to commit racketeering, according to the indictment.

Parents who hired Singer as part of the scheme allegedly paid between $15,000 and $75,000 per test, the indictment states.

"I want to communicate to everyone that I am profoundly sorry for the damage I have done and grief I have caused those as a result of my needless actions." Riddell said in a statement Wednesday provided by his attorney. "I understand how my actions contributed to a loss of trust in the college admissions process. I assume full responsibility for what I have done."

CNN has reached out to Williams and Dvorskiy.

The case of Felicity Huffman allegedly describes this type of scheme.

Huffman, an Academy Award nominee, has been charged with felony conspiracy to commit mail fraud and honest services mail fraud, according to court paperwork filed Monday in federal court in Massachusetts. She was arrested without incident at her home, the FBI said.

She is accused of paying $15,000 to Singer's fake charity to facilitate cheating for her daughter on the SATs, the complaint says.

A cooperating witness told authorities he purportedly traveled from Tampa to a West Hollywood test center to administer Huffman's daughter's exam. She received a 1420 on her test, which was 400 points higher than a PSAT taken a year earlier without the same administrator, the complaint states.

Huffman discussed the alleged scheme in a recorded phone call with Singer, the complaint says.

Bribing coaches for spots

College coaches do not explicitly decide who gets accepted into their university. But they do recommend to the admissions office certain recruited athletes to be accepted.

Being a recruited athlete in a Division I sport is a "very powerful influencer" in the admissions process, said Sara Harberson, a college admissions expert and former dean of admissions at Franklin & Marshall College.

Rick Singer walks into the John Joseph Moakley United States Courthouse in Boston on Tuesday.

Because of that, a second part of Singer's scheme was to bribe college coaches and athletics officials. In exchange, they would recommend to admissions officials that certain students be accepted, even if the student didn't play the sport and had false athletic credentials.

"I was bribing coaches for a spot. And that occurred very frequently, your honor," Singer said in federal court.

The case of Lori Loughlin, who played Aunt Becky on "Full House," illuminates this aspect of the alleged scheme.

Loughlin and her husband, fashion designer Mossimo Giannulli, face charges of conspiracy to commit mail fraud and honest services mail fraud, prosecutors said.

The couple allegedly agreed to pay bribes totaling $500,000 in exchange for having their two daughters designated as recruits to the University of Southern California crew team.

The daughters were recruited as coxswains even though they did not row competitively or otherwise participate in crew, the complaint says. The parents sent Singer photos of each of their daughters on an ergometer, the rowing machine, the complaint states.

Singer then facilitated bribes to Donna Heinel, the senior associate athletic director at USC, who got the students into USC as recruited athletes, according to the complaint.

"I wanted to thank you again for your great work with [our older daughter], she is very excited and both Lori and I are very appreciative of your efforts and end result!" Giannulli allegedly wrote in an email to Singer included in the complaint.

Giannulli was arrested without incident, and the FBI served a warrant for Loughlin, but she was not home at the time, an FBI spokesperson said. Loughlin was on a flight to Los Angeles, where she was expected to surrender at the Central District Court later Tuesday afternoon, according to a law enforcement source

CNN has contacted Iconix Brand Group, which owns Giannulli's namesake fashion company, Mossimo. CNN is also working to get comment from the actresses' representatives.

USC said it has terminated Heinel in the wake of the charges.

"We understand that the government believes that illegal activity was carried out by individuals who went to great lengths to conceal their actions from the university," the university said. CNN has reached out to Heinel for comment.

False charitable donations

As part of the scheme, Singer disguised the bribe payments from clients as charitable contributions to the Key Worldwide Foundation, or KWF, a nonprofit that Singer set up as a charity, prosecutors said.

But rather than go to charity, some of that money was instead used to bribe coaches and athletics officials as part of the scheme, prosecutors said.

"Singer's foundation purported to be a charitable organization, but was actually a front Singer used to launder the money that parents paid him," said Lelling, the federal prosecutor in Boston.

JUST WATCHED FBI: Parents paid up to $6.5M for guaranteed admission Replay More Videos ... MUST WATCH FBI: Parents paid up to $6.5M for guaranteed admission 00:51

Afterward, a KWF employee would mail letters to the clients thanking them for their donations.

"Your generosity will allow us to move forward with our plans to provide educational and self-enrichment programs to disadvantaged youth," the letter said, according to prosecutors. The letters also falsely wrote that "no good or services were exchanged" for the donations, prosecutors said.

The alleged false nature of the charity is evident in a recorded phone call on October 25, 2018, between Singer and Giannulli that is included in the complaint.

Singer, acting at the direction of law enforcement officials, clarified with Giannulli that the money they sent was in fact used to get the daughters into USC for crew, and Giannulli allegedly agreed. Singer then said that the IRS was auditing his charity and that they needed to get on the same page as to what they'd tell investigators.

"So I just want to make sure our stories are the same ... and that your $400K was paid to our foundation to help underserved kids," Singer said.

"Uh, perfect," Giannulli allegedly responded.

In addition, many clients then filed personal tax returns that falsely reported the payment to the KWF as charitable donations, according to federal prosecutors.

Singer's charity account, which contains $5.2 million, has been seized, according to prosecutors in court.