Fascia refers to the trim boards that cover the ends of rafters or roof edges. Those along the bottom of a roof are called eave fascia; they generally are nailed to the ends of roof rafters. Those along sloping sides of a roof are called rake fascia and generally are nailed to end rafters, trusses or extensions from those roof supports. Gutters are installed on eave fascia, and those boards are more prone to decay because of the water that runs off the roof and may soak into the boards if the gutter and roof's metal drip edge are not properly installed.
Test the fascia for damage by looking for peeling paint then poking the board with an ice pick, awl or long nail. If the board gives under that pressure, it is rotten and will have to be replaced. Check the entire length to see if all the fascia needs replacing or just one section. Measure the length of the fascia that needs to be replaced and the width to get an identical replacement board.
Remove the gutter by taking off any downspouts and prying off the metal straps or supports that hold it to the roof. Work from a step ladder or scaffold, which is preferable since it will cut down on moving the ladder. Have an assistant help you support the gutter during the removal process. If the gutter is in good shape, keep it for reinstallation; support it so it doesn't bend down to the ground.
Climb on the ladder and begin pulling off the rotted fascia with a pry bar. Rotted wood should come off easily. Use the pry bar to remove any nails once the rotted fascia is removed. Scrape away any debris behind the fascia. Check the condition of the rafters behind the fascia; if any are rotten, patch or replace them before installing new fascia. Rafter repair may require removing part of the roof to expose the rafter and may involve professional assistance.
Cut the replacement fascia board to size and lift it into place; this will require help if the fascia is very long. Tack it in place to the rafters at the ends then fasten it to all rafter ends with screws or nails. Check the metal drip edge on the roof eave before nailing the fascia in place. If the drip edge is bent or damaged, replace it before installing new fascia.
Replace the gutter, either with the old one or install new guttering. Check the old guttering carefully for leaks or damage; test it by filling it with water to look for seepage. Fill small holes with epoxy or a metal patching material.
Replacing damaged rafters will require professional help if the damage is significant. If the damage is not severe, remove any damaged wood and add short pieces of replacement board from the good portion of the rafter to the eave. Sometimes it may be possible to cut out a short section of the top of the rafter and cut a replacement piece to match that notch, then screw the pieces together.