Either you unlock a new garden plot or a fish farm, you should hire an employee (preferably with suitable skills for this specific position) to automatically produce and collect the goods needed to make the best sushi in town. 

However, you can also speed up the production if you do some extra work by yourself. Tap on a specific plot or fish farm not only to try which ingredient you want to produce there but also to skip some time planting or breeding fish manually. No matter if you hired someone, you can do it every time you want to collect some extra ingredients ASAP.