What are the best ways to play with my 12-month-old?

Get on their level. Playing with your children can be one of the most rewarding parts of being a parent. When you are considering a 12 month old, make sure you get on their level. If they are walking, walk with them, explore different parts of the house or the yard. Sit or lye on the floor with them and stack blocks, push cars or trains (any sound effects that you can add are always good:) read and look at books.
Muisc, Shapes, Dance. At around this age babies love rolling balls, playing with cups and wooden spoons (get those colorful stacking cup for visual/motor stimulation). Try also a maracas, while he will like the sound of it, he will enjoy more chewing the handle to sooth his swollen gums (make sure it's child safe with no lead coloring). Singing and dancing with him is also fun. Always have some background music around.
Follow his lead. You 12 month old is likely to move quickly from one activity to another. Try to follow his lead, and play with the toys that he prefers. Good toys to try are sorting toys, puzzles with big pieces with knobs, and simple musical instruments. Have fun!