Repairing rusted out steel spouting:
Cut out the damaged section of spouting by running 32-teeth to the inch hacksaw through the front and into the bottom. Continue this cut with a pair of straight tinsnips. Then try and get the straight tinsnips into the back of the spouting and if not all the way through finish with a sharp carpenters wood chisel to cut the final section of the cut out. Repeat on the other side of the damaged area and remove the spouting out of the brackets.
Take a small section of this spouting down to your local roofing or sheet metal shop and try to get a new match for it. Take this new piece and cut it 4 inches (100 mm) longer than the missing spouting gap. Then clean the joints with rags and hold back any water with other rags. Open up the bead of the very top of the front of the old spouting and place a line of silicone into both joints then place the new section into its new home and close off the bead crunching it back down with a pair of pump pliers. Now take a 3-inch (75 mm) nail and placing it above the back join against the wood fascia bend it over to hold down the very back of the joint together firmly.
Then place rivets in the front and in the bottom and smear these with silicone on the inside of the joint and swirl around in figure eights over the internal joint. Repeat on the other joint. And remove rags and the job is done. If you need to go around a corner with your repair just have the local sheet metal shop make you up this angle.