Federal cases are not as publicly accessible as state court cases, but the information is available if you know where to look.
The starting point is knowing which federal district the case is in. Federal charges are filed in one of 94 federal judicial districts across the country, organized by geography. If your person was arrested in Miami, the case is in the Southern District of Florida. If it was in Chicago, it is in the Northern District of Illinois. Knowing the district is the key that unlocks everything else.
Once you know the district, contact the clerk of that federal district court. The clerk's office maintains the docket for every case filed in that district, and court dates, filings, motions, and case status are all part of the public record. Most federal district courts also have their electronic filing system accessible through PACER, the Public Access to Court Electronic Records system at pacer.gov. For a small per-page fee you can pull up the entire docket for the case including scheduled hearing dates, filed documents, and case history.
The fastest way to find out which district is involved is simply to ask your person directly. They know what they were charged with and where the charge originated, and that information tells you exactly which district court to contact. Federal defendants are always informed of the charges against them and the jurisdiction handling their case.
If they are being tight-lipped about the details, the federal inmate locator at bop.gov lists the district of sentencing for convicted inmates, which at least points you toward the right court.