The best time to climb Monch is between April and September, when the weather is likely to be clear. That being said, the terrain is quick to recover from storms, and climbing out of season will guarantee you a peaceful trip.
You will need full climbing gear for this ascent, including mountaineering boots, an ice axe and trekking poles. Make sure you pack at least 1 litre of water.
If you are concerned about altitude sickness then opt for a two-day climb, with an overnight stop at the Mönchsjoch Hut.