Mecha-Naruto Story is an additional mode in the Ninja World Tournament - most of your items from the "regular" tournament won't be available to you, meaning that you will have to get them again, if you want to use them. Additionally, you are limited to Naruto (most of the time) character only, because the whole story of this mode is concentrated on the interaction of this hero and the titular Mecha-Naruto.
You will start at the entrance to the village, near which there's a character you must speak with, to start your journey. Talk with Hinata, to, after a long conversation and a series of short cutscenes, regain control of your character. You will learn that you are currently in the Festival Island, or to be more precise, on the terrain belonging to A Rank. It's a chance to explore this part of the island, because after you finish your quest here, you won't be able to get here again unless you've finished B Rank of the Ninja World Tournament. Most of the entrances here are locked, and the only things you will have access to are hidden treasures. You can easily ignore it, as there are only a few of those treasures here.
You should now head North, to rejoin Hinata, after which a long series of cutscenes will initiate, during which you will meet Mecha-Naruto.
After going back to the village, you will regain control over your character - save the game and run down the stairs (to the North of your actual position), to initiate another cutscene. The next day you will have to, yet again, join Hinata and Mecha-Naruto by the village entrance. Before you do so, you can use the opportunity and look around the village. It's divided into several section, and most of them hold something of interest, like shop, or lottery. If you want to look around the village, you can search for various treasures scattered around, but there's nothing of any importance to found. Otherwise, go straight to the mentioned gate, start the conversation with Hinata and go to the next chapter - "Mecha-Naruto - qualifying round".