I bought some items but my Toribash remains the same. I wonder how I do it and how I see the items I bought.

Go to Shop -> Deactivated -> Press Activate next to the name of the item(s) you want to activate

Also, after you do what Tonakai suggested, if you want to see what items are on your Tori, click the Activated icon and you'll see specifically which items are on it.