Take the lift up to the Plan de l’Aiguille and head downhill on eroded switchbacks to a cute restaurant a couple hundred yards below. The scenery is already stunning in all directions.
Follow signs for Montenvers and traverse across towards the Mer de Glace glacier. It rolls a bit but is never taxing. You start just above treeline, but near the end you'll get into more vegetation and a prettier section of trail, if that's possible.
When you get to the trail junction with the Signal Forbes
Trail, go left for an easier and faster route to Montenvers, or head up the Signal Forbes
Trail for even more stunning scenery and MUCH better views of the Mer de Glace.
Once at Montenvers, take the tiny tram down to the glacier and explore around. The well-documented glacier retreat is terribly sad. Find the sign that indicates where it was when you were born, and you'll realize just how fast the glacier (and world) is changing.
You can either hike back to Chamonix or take the train, like most folks.
This trail is immensely popular, so it's a bit rough and crowded, but well worth that small price.