Use a nail puller to remove nails near the damaged sections of the wood siding. You will have to cut through the nails using a hacksaw blade slid underneath the wood siding if the nails are not easily accessible.
Place a chisel underneath the damaged wood siding panel and apply a small amount of pressure on the chisel. This will slightly lift the panel so that you can easily insert a pry bar and thus remove the damaged panel. Be careful in order to prevent damage to neighbouring panels. If the area to be repaired is small, you can simply cut out the damaged part.
Take measurements of the empty area and purchase replacement siding panels accordingly. Alternatively, you can use damaged panels that you removed earlier as template for buying replacement siding panels.
Cover the revealed area with building paper and drive roofing nails through it with a hammer to hold it in place. The building paper will prevent moisture from affecting you repair work.
Use a sharp knife to transfer outlines of the damaged siding panels onto the replacement siding panels. Alternatively, you can take help from the measurements that you took earlier. Cut and reshape the replacement siding panels accordingly.
Position the replacement siding panels, one at a time, at their appropriate location on the wood siding. Drive galvanized siding nails through the replacements siding panels to secure them in place. For added stability, draw nails through the siding panels and into the studs whenever possible.
To get rid of nail holes and vertical seams, fill in caulk with a caulk gun.
Apply a thin coat of wood primer on the newly installed wood siding panels, wait for the coat to dry completely and then paint the panels. Be sure to use the same shade as the rest of the siding.