Install drop ceiling hooks onto the bars between the ceiling tiles. These specially made hooks clip on either side of the bar by first inserting one arm under the bar and pressing the other arm under the other side. These hooks hold up to 30 pounds and can be relocated when you change the room.
Unbend a paper clip and wrap the end around the ceiling tile bar. Form a hook with the paper clip wire and hang lightweight items on it.
Use tape to secure light items to the center of the ceiling tile. Attach the item, such as a child's drawing on paper, to a piece of string and tape it to the ceiling by crisscrossing an "X" over the end of the string. This method won't provide a long-term solution.