You need a bee smoker to smoke the bees, so you can collect the honey.
There's a blueprint on the shed table. It has five things you need to gather. Use the items from your inventory on the corresponding places on the blueprint.
Spout, to target the smoke
Bellows, to pump some air
Canister, to hold the fuel and the heat
Fuel, from: A. Cotton, that is usually used in clothing B. And pine needles
When the smoker is ready, you need to light the fuel to use it.
Pick up the red funnel. It will work as a a spout.
Use the bike pump from the right of the shed.
Pick up a metallic paint can. Use that as the container.
Open the wardrobe and use the wedding dress as cotton.
Guide listing help
Unlike normal walkthroughs, in Nice Game Hints you can select just the puzzle you want hints for. Here are listed the puzzles for "Building the smoker" in The Will of Arthur Flabbington. The guide you choose only contains information about that puzzle, reducing possible spoilers for other puzzles.