What you will need:
2 item frames
Fuel source (coal)
Item to be smelted
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Start by building the right side of the smelting system with five cobblestone blocks. Put an item frame on the top cobblestone block.
Place a chest to the left of the top most cobblestone block. Leave one empty space to the left of the chest. Then, make another cobblestone tower, this time with only four blocks. Place an item frame on the top cobblestone block.
Place 3 cobblestone blocks directly under the chest, starting on the bottom or ground level. This is so you can place a downward facing hopper underneath the chest. You can destroy the 3 cobblestone blocks as soon as the hopper has been placed, but leave the block directly below the hopper for the next step.
Then, place a single chest between the hopper and the item frame on the left.
Either replace or leave a cobblestone block directly under the hopper for this step. Place a new hopper below the second chest, the one on the left side of the screen. As you place the hopper, point your cursor toward the cobblestone block that is under the first hopper. When you place hopper #2, the bottom should look like it's going into the cobblestone block.
Once this hopper is placed, remove the cobblestone block and put a furnace in its place, directly under hopper #1.
Place another cobblestone block as a placeholder on the right hand side. Place a hopper on top of it, facing down. If you don't have the cobblestone block as a base, it will be hard to place the hopper facing down. You can get rid of that cobblestone block as soon as the hopper has been placed.
Place a permanent cobblestone block to the left of the third hopper. Then, place a chest beneath the third hopper.
Place the item that you want to have as a result of smelting in the top-most item frame. So for example, if you want to smelt iron ore into iron ingot, place one iron ingot in the item frame on the right.
Place your fuel source in the item frame on the left.
Add the iron ore to the tallest chest on the right hand side, the one near the iron ingot item frame.
Add your fuel source (coal) to the chest on the left side. Your furnace should turn on.
Check the bottom chest on the right and see smelted iron ingot inside!