I taught someone else Oh My Goods today, and I think I finally have a solid teaching pattern. It helped that they were a math major who learns things quickly though.
1. Prepare by having 3 example cards for different production chain setups. 1 example card that takes a resource and makes a 2-coin good, 1 example card that takes charcoal + a resource, and 1 example card that takes 2 goods.
2. Tell players to only pay attention to the cog and the coin at the bottom of a card. Explain that each card is a building, and buildings make goods.
3. Explain facedown cards represent goods. Put 4 facedown cards on charburner, ask how many goods? (people say 4)
4. What is each good? Explain the symbol in the gear, so you have 4 charcoal.
5. Explain each good is worth coins, shown under the gear. How many coins? (people say 4) Use another card as an example, e.g. 3 cards on flour building for 2 coins each, how many coins? (people say 6)
6. Explain squares on right are resources feeding production chains, which let you produce more goods. Give example of playing wood from hand on starter building.
7. Explain gears on right are goods feeding production chains. Give example of a building with charcoal from table + card from hand, and show that it produces 2 goods on the building. Calculate the coin gain (e.g. 1 coin to 4 coins).
8. Give example of a building with two production goods driving the chain. Remind everyone that BOTH goods are required.
9. Explain that these chains are nice, but there is a catch. The symbols on the left have to kickstart production before a chain can activate. Those symbols can come from your hand or from the market.
10. But what's the market? At this point, you can start the first round. Mention that people can throw away their hand and replace it -- suggest this if people don't have cards that match their starter card's production symbols (e.g. wood and wheat, or wood and cotten, etc.). Deal everyone 2 extra cards. Explain the rest of the game in order as the rounds happen.
11. After a round or two, the assistant rules and the extra final round with all production chains can be explained.
It looks like a lot when written this way, but I think each step is simple and leads into the next. This seems better than trying to do the game round in chronological order when people get lost looking at their cards.