With a grand jury subpoena, Mueller can obtain physical evidence, such as documents, memos, handwritten notes or audio recordings, or he can request testimony.
In the case of Mueller's investigation, testimony is key, said civil rights lawyer and NBC legal analyst Maya Wiley.
While subpoenas are a "crucial way of getting information," getting people under investigation to admit to smaller crimes, such as perjury, or catching them in the act can get Mueller a lot farther, Wiley told CNBC in a phone interview.
Like he did with Flynn and former Trump campaign aide George Papadopoulos, "you start with low-level crimes and then say, 'We'll get you on more,'" Wiley, also a social justice professor and MSNBC contributor, explained. (Papadopoulos served a 12-day sentence last year after admitting he lied to federal investigators.)
Then, if the suspect knows there are larger crimes or connections to conspiracy, he begins to cooperate, she said, and not just by telling prosecutors what he knows, but handing over his emails, meeting notes and correspondences with involved parties.
"From a legal standpoint, you see the case being built on smaller crimes in order to get people to volunteer information," Wiley said.
Another tool Mueller can use is interviewing witnesses, said Rossi, a former Justice Department official who trained several of Mueller's aides. In a phone interview with CNBC, Rossi estimated that the special counsel's team has interviewed thousands of people for the investigation.
A third way Mueller can gather evidence is through a wire tap. In special cases, especially those involving potential national security risks, Mueller can obtain search warrants through the Foreign Intelligence Surveillance Act, or FISA, a law that allows physical and electronic surveillance of foreign agents or powers.
With FISA power, Mueller can monitor correspondence, such as emails and text messages, between persons of interest in real time, provided the communications aren't encrypted.
Other investigation tactics can include getting standard search warrants, obtaining a court order to view a suspicious party's tax returns, or sending undercover officers or cooperators to gather evidence in the field, Rossi said.
Seth Waxman, a former federal prosecutor now with Dickinson Wright, told CNBC, "The biggest thing for prosecutors, especially in white-collar cases, is a paper trail."
That paper trail usually consists of bank records, emails and text messages. Investigators can subpoena phone toll records, which will give them the phone numbers a person called, but to actually read emails or texts they need a search warrant, which requires probable cause.
On its own, a paper trail can be confusing for a jury, while testimony may be seen as suspect, Waxman said in a phone interview. But combining the two can "breathe life" into an investigation, he said.
"The paper trail is what begins an investigation and provides background and foundation for it," Waxman said. "The cooperators then breathe life into that story and tell it in a way that's compelling."