Not all crimes are considered a federal offense. In order for the federal authorities to get involved, a crime must violate established federal law or be committed against the federal government or federal government-related officials. A bank heist can be considered a federal offense if the bank that was robbed was a federally insured bank.
Also it should be noted that there are multiple federal enforcement agencies, each with their own responsibilities and jurisdictions. Therefore, it is the nature of the crime that has been committed that determines which federal agency has jurisdiction.
Officers from that federal law enforcement agency, who are generally referred to as special agents, can arrest an alleged suspect after obtaining an arrest warrant. However, they also have the ability to take a suspect into custody without a prior arrest warrant. In some instances, they may even delay an arrest in order to obtain additional evidence.
In situations where the crime is considered a white collar crime, often times federal agents will need to obtain documents and paperwork from not only the alleged suspect or suspects but also those individuals who claimed to have suffered harm. To do this they can obtain a search warrant from a judge or get an a subpoena from a grand jury.
A grand jury essentially functions like a regular jury in that they are a group of people that are selected from the community who have been tasked with the responsibility of determining whether a crime has been committed. To help facilitate this, they can issue subpoenas to anyone who may be relevant to the case. Once a grand jury has viewed enough evidence to conclude that there is probable cause then a charging document, better known as an indictment, is issued.
The federal crime process involves an arrest, initial appearance, arraignment, discovery, plea bargaining, jury selection, trial and potentially sentencing.
Source: Federal Bureau of Investigation, "A Brief Description of the Federal Criminal Justice Process," Accessed June 1, 2015