Read a Book
Read an age-appropriate book with the toddler you're babysitting, using different voices for the different characters. Choose a picture book, since pictures help to tell the story for young children. If you have books for young children on hand, bring them so you know you'll be prepared.
Art Projects
Let the toddler color with crayons and a coloring book or sketch pad. Cut out different shapes from construction paper, and let the child paste them onto a piece of paper to create a design or a picture. Create your own pictures as well; the child will probably be delighted to see what you've created, especially if you include her in the picture. Or, make play-dough and let the toddler practice forming shapes with her hands or other tools, as described on the University of Illinois Extension's website.
Gardening
If permitted, help the two-year-old do some simple gardening, such as watering flowers around the house and patio. Instead of hurrying, stop to talk about the nature all around you, noticing the calls of birds, small animals or insects you see, and the smell of the flowers in the garden.
Puppets
Stage a puppet show for the two-year-old, acting out one of his favorite stories. If you don't have puppets, use dolls or stuffed animals. Or, make the puppets together from household supplies like paper bags, construction paper, yarn (for hair) and glue. Talk to the child with the puppets to involve him in the story, with the puppets asking questions like, "What can Cinderella do now?" or "Who do you think Snow White met in the woods?"
Music
Find a small musical instrument to bring with you, or use a musical toy the child already has, to explore music together. If you have small maraccas, a hand drum or other small percussion instruments, put together a bag of instruments to bring with you. The two-year-old will enjoy experimenting with the different sounds, as you sing or play a melody along with her.
Playing with Blocks
Engage with the child through games or toys he enjoys. As the Babysitting Tips website says, two-year-olds often enjoy playing with blocks, and you can build your own creations to entertain the child. This activity also helps children to hone their coordination.