Purchase a plastic barrel with a spigot attachment or the ability to have an attachment installed. Clean the barrel thoroughly of tar, dirt and creosote. Use a wire brush to remove the tar and creosote.
Lay the chicken wire on a smooth, flat, vertical surface. Turn the barrel over so the open end rests on the chicken wire. Measure 4 inches out from the barrel along the wire at various points around the circumference of the barrel. Use the permanent marker to trace a circle on the chicken wire around the barrel connecting the markings made by the measurements.
Remove the barrel. Cut the outline of the circle on the chicken wire with the wire clippers. This becomes the cover preventing leaves and debris from mixing with water and clogging the spigot. Turn the barrel upright.
Cut a 4-inch wedge into the chicken wire cover large enough so you can bend the chicken wire. Put the cover over the barrel. Line up the cover evenly over the top of the barrel. Bend the edges of the chicken wire over the lip of the barrel so the cover fits snugly.
Set up two cinder blocks under the shortened downspout with the open sides facing up to provide greater stability. Place the barrel on top of the cinder blocks underneath the downspout. Visually center the barrel under the downspout.
Drill a hole 2 inches from the bottom of the downspout. Insert the eye bolt into the hole with the head being inside the downspout. Screw the eye bolt to the downspout by threading the nut onto the eye bolt stem until it is against the downspout.
Attach one end of the chain to the eye of the eye bolt. Let the chain drop down through the wedge in the chicken wire into the barrel. The water droplets will travel from the downspout along the chain into the barrel. This provides an efficient water delivery system to the collection barrel.
Set up the drip irrigation pump under the spigot. Attach the pump to the spigot. Connect the water hose to the other end of the pump.
Run the water hose to the growing area. Set up smaller hoses near where the plants are or will be; make sure the hoses are close to the roots to ensure they get the water. Put the emitters onto the smaller hoses. Put the cap on the end of the main hose to keep from losing water and pressure.
Fill the barrel halfway with water. Turn the spigot on and start the pump. Check for leaks at the spigot and pump. Adjust the emitters as needed for the plants.