To start a business with the Merchant, you need to obtain a Trade License. You buy the Trade License once you have reached the rank of 'Rightful Citzen' at your church.
Once you have the trade license, head to the village on the day that the Merchant appears and hand it over. He will then open up a little room just behind where he normally stands and give you more instructions and information on how to grow the business.
If you are a super prepared person, it's good to have your gardening and alchemy/book making set up properly back at your home base as it will make the follow-up trophy to get a 5 Star business easier.