What are the best ways to play with my 6-month-old?

Child proof at 6 mo. A 6 month old is quickly becoming mobile. He can now roll everywhere, he is learning to sit, and he is putting everything he can get his little hands on in his mouth. You do not want to discurage this as the use all thieir senses to explore. You want to make his area of discovery safe. Childproofing as your baby is reaching this stage will help you prevent issues as he continues to develop.
Cause and effect. Now they dicover cause and effect. The sit in the high chair and throw things on the floor repeatedly, and we pick it up multiple times, build on that with different activities. They learn dexterity by transfering objects from one hand to the other, everything, goes into the mouth as they use this as one of their senses, work with differenr flavors and textures. They are rolling help them discover.
Sign Language. At 6 mo they understand more than they can verbally express, and they innately develop their own sign language. You may see him repeat certain hand and arm movements when he wants something, or when he is tired for instance. You can easily teach the baby new signs, he will quickly associate what you are verbally saying with your hand movements. It is an easy way to help your baby communicate.
1-on-1 interactions. Six month old babies like to play. Activities that make a baby smile are good to continue, such as holding/cuddling the baby, gently teasing the baby with a stuffed toy, singing a song to the baby, talking to the baby, a brief baby massage, playing peek-a-boo, etc. At 6 months, some babies can roll towards a toy to grab the toy. Some babies can mimic waving or clapping.