Following you child's lead is such an simple strategy, but it is surprisingly underused. If a child sees that an adult is interested in the same thing as them, they are more likely to let that adult in to their play. Once an adult has been let in, they are in a much better position to encourage and support the child with their language development. This can be used with children of any age and ability, from new babies to teenagers.
The easiest way to do it is to simply stop, sit back, and see what your child opts to do when adult input is at a minimum. Look to see if they choose a particular activity. Depending on your child's age and stage, this could be anything from cooing, babbling, crawling, clapping or jumping, to playing with dolls, playing with cars, dancing, or racing in the garden. Show your child that you are interested and see if you can find a way to join in. It's as simple as that! Once your child has let you in to their activity, you can gradually start to adapt the activity to work on turn-taking, attention and listening skills, new vocabulary, and many more communication skills. Make sure you don't change the activity too much though - your child needs to stay in charge most of the time to keep them interested and motivated.
This brilliant video by Phoebe Caldwell demonstrates Intensive Interaction, an approach which has following the child's lead at its core. Phoebe is a specialist in Intensive Interaction. In this video, she uses it with Ricky, a young man with autism.