What are the best ways to play with my 11-month-old?

Variety. 11 mo olds like to play patty cake and other interactive games, many are cruising and trying to walk, so they enjoy new environments to explore. By 9 months, they understand object permanence, so you can have some fun with baby guessing what's underneath and moving things with that new pincer grasp. Get down on baby's level and if you are having fun playing, s/he will too.
Read, sing, dance, sort. Language and undestanding are exploding, as is imagination, they can start playing pretend, and will laugh when you pretend to drink out of their sippy, give them easy one step commands to help them with task and understanding. Sing and dance with him, it will help him develop coordination and rythym. Point out everything you hear and see to him, help him sort and see similar objects. Always read.