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Figure out where to connect it by setting the barrel on the platform next to the downspout. It should be close enough to the downspout that you can connect it with the downspout elbow. Mark the downspout one inch below the height of the rain barrel. You'll need to attach the downspout elbow to the downspout so water will pour directly into the barrel. Use a hacksaw to cut the downspout at the mark. Fit the elbow to the downspout. Fasten it in place with screws, and make sure they're tight. As your measuring and fitting the elbow to the downspout, make sure that the end of the elbow will dip well into the barrel so all the water gets collected there. You don't want the water to be pouring into the barrel from above. If the barrel has a lid, use the hacksaw to cut a hole large enough for the end of the elbow to fit inside. Cover the area around the hole with the metal screen. This will prevent leaves and other debris from running down the downspout and creating a clog in your rainwater collection system. If you have more barrels, set them on the platform and connect lengths of hose to the valves.

Summary:
Connect the downspout elbow to the downspout. Connect the barrel to the elbow. Place a filter at the top of the downspout. Connect the additional barrels.