Remove any existing soffit ceiling and inspect the boards on both sides. Replace any wood that is rotted or otherwise damaged. Measure the width of the soffit opening to get the right side panels; most soffits are 12, 16 or 18 inches wide, and aluminum panels come in those widths.
Install J-channel molding, with nailing slots on the top and a groove to hold one end of the aluminum soffit panel, on the house wall, typically on what is called a frieze board nailed on the top edge of the house siding. Overlap sections of J-channel by 2 inches as needed to cover the length of the roof. Drive aluminum shingle nails into the centers of the nailing slots, loose enough for some movement.
Inspect the facing on the rafter ends to decide on how to fasten aluminum soffit ceiling there. Remove an outer fascia or facing board if one is installed over a subfascia board that is nailed to the rafter ends. Nail panels into the bottom of the subfascia. Install F-channel molding on the fascia if it is the only outside board; nail this to the outside of the fascia with the connection slot facing in.
Slide the soffit panels into the J-channel and either nail them through nailing slots at the fascia or slip them inside the F-channel grooves. Snap the panels together at the joints; soffit panels typically are made to interlock with an edge on one side that slides into a slot on the next panel. Install a new fascia board if panels were nailed to the subfascia or a 2-inch trim piece to cover the nailing points on F-channel.