Purchase or prebook round-trip train tickets from Interlaken Ost to Jungfraujoch. Prebooking is highly recommended due to limited availability and high demand.
Travel by train to Saint-Gervais-les-Bains-Le Fayet through Geneva, then transfer to local train or bus to Chamonix. Booking the Nyon-Geneva and Geneva-Saint-Gervais segments in advance is recommended for cheaper and assured seats.