The Stream Treasure Map
To catch a River Trout you can use a regular Bamboo Rod or Carbon Rod. The Trout are a medium-sized shape in the water and they like to snack on Worms, Maggots, Bee Larva, and Fish Eggs. After you catch the fish bring it back to her and she'll give you a Treasure Map.
The map will tell you to go East 30 paces from the Jizo, north 10, west 5. That spot will be directly underneath a tree. Examine underneath the tree and you'll find something buried. Then the errand is over.
Your new rival
To beat Naoko at her game you need to catch an Ayu that is 8 inches or larger. Once you have the fish return to the bridge and talk to her. If you win then she will reward you with the recipe for Salt Grilled Ayu.
Learn how to swim
After the errand has been completed you can now swim through water just by walking through it. Old Smarty will only teach you how to swim if you have the "No Swimming" entry in your Diary. As you level up your character, your swimming technique will increase. The higher your swimming technique, the faster you can swim. When you wade through the water you will loose Hit Points.
Remove the boulder
Back at Smarty's place, the old man talks about a little shrine near the boulder. If you put an offering into the shrine the boulder might move. Smarty then falls asleep again, so Kayo has to tell you the fish needed is a Yamame.
Catch a Yamame in the area west of the wood god's shrine. The fish needs to be above 12 inches else the little god won't listen to your request. When you put the appropriate sized fish into the shrine the wood god will remove the boulder that leads to the Mountain map.
Find the Bottled Recipe owner
Take the bottle up to the Mountain map. Follow the path until you reach the bridge, but instead of going across the bridge follow the lakeshore to the east. You will find a girl with braids, wearing a brown sweater. Shizu admits to putting the recipe in the bottle and floating it downstream. She did it in an attempt to teach the local fisherman how to cook. They are all very terrible chefs!
Back at the Stream, Minoru tells Shizu that he found her recipe. He then asks if she'll cook for him forever as his wife. Shizu accepts Minoru's proposal. To reward you for your assistance Minoru will give you the recipe for Butter Grilled Big Iwana.
Harvest Sprite happiness
After he leaves you discover that the item he gave you was a ??? Seed. In your Diary you'll see that you have completed part 1 of The Straw Millionaire errand.
The Great Duel
Take the invitation to Takako, who is blocking the path to the Field map. She is disappointed that Yoko was too chicken to come herself. Takako refuses to move from the path until you bring Yoko to her.
Yoko explains the whole conflict started over some food that she had given to Takako. She thought it would be a good birthday present but it turned out that Takako hated the food! Yoko will help you get her to move if you find out what food Takako likes. After talking with Takako you find out that she likes Salmon.
Catch a Salmon from the Mountain map and give it to Yoko. She will make a meal to give to Takako. Yoko gives it to the grumpy junior and all is forgiven between the two of them. Now you can get to the Field map. Yoko also rewards you with the Boiled Prawn Recipe and the Blackened Newt Recipe. You may have already received the Boiled Prawn Recipe if you had participated in Sachiko's Black Bass Festival back on the Mountain.
This errand will be available after you go through the Mountain and help Naoko catch the Great Brown Trout.
Mamoon the Curry Chef
The Itou are around the Waterfall in the Stream. Use your washtub to float out to the waterfall, and wedge yourself against the wall so you don't float away. Then just equip a bait rod, a Small Fish, and toss your line into the middle of the Waterfall. Eventually (and with some patience) you will catch the Itou. Take it back to Mamoon and he will request a Cherry Salmon next.
The fish can be found just south of the Waterfall and there's plenty of them. Bring the Cherry Salmon back and Mamoon will request his last fish. He needs a Prawn to complete his curry dish. The Prawns are in the darker water of the northern pond in the Field map. When Mamoon is finished cooking he will unblock the path to the Rapids, and drop the recipe for Raw King Carp.
Stream Cooking Contest
The contest is difficult to win if you aren't at a good level of cooking skill. You will most likely win if you are at Decent level. The easiest recipes to use are Salt Grilled Ayu, Goby (Haze) Tempura, and Fried Kajika. All 3 of those fish can be found in the southern waterways of the Stream.
If you win the contest, Bearnaise will invite you to participate in their main contest but you are required to have at least a Pro level of cooking skill or higher before you can participate.