What are the best ways to play with my 7-month-old?

Explore the world. At this age, your baby is interested in everything going on in the world. Explore things - name things, sing, dance, go outdoors and explore, use everyday experiences as teaching moments - just play. Toys are vastly overrated! if you do use play enhancing toys, try to go green and use toys that are made of safe nontoxic materials.
Interaction. Interaction between you and your baby brings a lot of pleasure to both baby and parent. It also teaches the baby appropriate emotional responses. For instance, if the baby makes a funny face and you laugh or the baby bites you and you wince she learns which of her behaviors results in what response. Playing peek a boo teaches object constancy. Video screens are no substitute.