Begin by installing trim pieces before slipping the soffit pieces into the trim and nailing them. Then, install the fascia to cover the outside edge of the pieces and to protect the wood subfascia.
If the roof has wood framing in place for the soffit, nail a piece of J-channel in place tightly against the wood framing using 1-1/4 inch shingle nails driven into the framing. The channel holds the ends of the soffits along the house and the short sides of the soffit. If there is no framing, use a piece of F-channel along the house. Soffits that are wider than 12 inches require additional wood support pieces down the middle to prevent the soffits from sagging. Using a carpenter's square, install the first and the last soffit panels perpendicular to the house before installing the ones in between the ends.
Use a piece of undersill trim to hold in place the top edge of the fascia. Alternatively, hide it behind a piece of drip-edge or other roof-edge flashing. Normally, you must trim the top of the fascia so that it fits between the soffit and the edge of the roof.
Regardless of the material you are using, installing soffit and fascia follows the above instructions.