It is of no concern to your 1-year-old whether the toys you give him are fancy imported ones or empty oatmeal boxes and paper cups. Consider giving up a low shelf in the kitchen (or buy a small laundry basket), and keep it filled with a changing assortment of unbreakable plastic cups and spoons, well-cleaned plastic food containers (like some margarine tubs), plastic ice cube trays, and other containers. These should be his materials to use as he pleases. Vary the supply by adding new objects occasionally and removing the things your child seems to be bored with.
One-year-olds also love to explore processes and the relationships among things and events. That's why repeatedly opening and closing doors and boxes holds such appeal. (Drawers, while also fascinating, pose a greater safety risk and should be avoided.) Be sure that the doors your child plays with have special safety catches to prevent them from closing on tiny fingers; these are inexpensive and easily found at hardware stores. And remember the drawers and cabinets that should never be accessible to children: those containing sharp implements, household cleaners, or other dangerous items. These should be securely fastened with childproof safety latches.
Books will also fascinate your little one -- largely because they too can be opened and shut. Sturdy cardboard board books or spiral-bound baby books are ideal for this use. To help her manipulate the heavy pages, punch a hole in the corner of every other page and tie a piece of yarn through each hole. This will separate the pages a little bit and make it easier for your baby to grip them.
Other processes, too-turning a light switch off and on, filling and emptying cups and bottles in the bathtub, or any exploration of cause-and-effect relationships -- will delight your young experimenter. Pop-up toys such as jack-in-the-boxes may startle your child the first few times the character leaps up, but she'll soon be thrilled with the discovery that she made it happen -- and that she can do it over and over again.
Obviously there are times when it will be inconvenient to have a young Einstein underfoot in the kitchen or a miniature Madame Curie conducting an experiment on how loudly -- and how often -- she can bang a frying pan against the floor. Within reason, give her free rein -- virtually every experience has the potential to teach your youngster something. Setting behavior limits is essential, however, and anything detrimental to her safety, to family property, or to your peace of mind should be beyond those limits.