The nearest rail station to Cambridge Corn Exchange is Cambridge rail station, which is a 20-30 minute walk to the theatre at buggy pace. Alternatively you can take the Citi 3 bus route from outside the station. It takes around 15 minutes and stops on St Andrew's Street, a few minutes' walk away.
Lots of other local bus routes stop on St Andrew's Street too. Use Google Maps to plan your journey by public transport before heading off, and please leave plenty of time!