What are the best ways to play with my 2-month-old?

Eyes and tummies! Your baby wants to look at everything, but especially your eyes. Get close to her face because she can't see very far, then show her your face, your expressions. Also, frequently put her on her tummy on a safe flat surface, then get down at her eye level and slowly raise your head so she will push up to look at you. This helps her gain head control. Don't ever leave her alone in this position.
Talking, touching. At 2 months, a baby is very young and doesn't do much playing. A parent should spend time talking to the baby, making eye contact with the baby, cuddling and stroking the baby, and gently playing with the baby's hands and feet.
Engage! Talk, sing, smile, laugh! Engage your child as much as possible. In the coming months, you will find babies at this age will focus on your eyes and face and the early speech they hear now will be the foundation for their speech later. Know that infants are, in essence, nearsighted and being close will help, but they can see further objects, especially if there are good contrasting colors.
Have fun! Put your baby on her back with brightly colored objects above. Talk, sing, and make faces at her. Put her on her tummy while you watch her. You can take a toy and try to get her attention and encourage her to lift her head. See if she will turn her head to your voice as you sing or talk from the side. At this age times awake are short, as is playtime. Get happy when she smiles!