How do you send a blue or green hero to the hall to work?

You can station development / production heroes in various buildings. To do this you need to build and upgrade the Town hall building. Tap on the town hall and choose the 'Station' option.

Each hero has a fixed cost to station it and your town hall will have a maximum cost that you can use to station the heroes. You upgrade the town hall to increase this maximum capacity.

If you have enough capacity you can Tap on the Station option next to each of your available heroes to place them in the appropriate buildings. Then unlock and upgrade the heroes skills to get their benefits while they are stationed.