Damaged roofing felt typically can be fixed by inserting a patch and sealing the hole. Start by lifting the torn felt and spraying roof and gutter sealant underneath. Allow enough time to dry according to the sealant manufacturer's instructions. Cut a square of matching roofing felt and insert it underneath the torn section. Lift the torn section and spray additional sealant between the patch and the torn section. Allow this to dry, then spray additional sealant on the joints.
If the damaged area is not at the edge of the existing felt, the same process can be used, except the patch may need to be placed on top rather than underneath the damaged felt. Make sure to spray sealant on the exposed roof, on the bottom of the patch, and around all of the joints. If there is any blistering, mold or rot, cut away the damaged section and apply a patch.
For more substantial damage, the entire section of felt may need to be replaced. This process requires removing the tiles or shingles from the area and removing the damaged portion of felt. Then a new section of roofing felt can be laid down, nailed in place, and sealed as normal.