The trailhead is at the bridge over the Irkut River where the Black and White Irkut flow together. (1800.7 metres) This is shortly beyond the gate (rarely manned) that declares the area off-limits to those (Russians and foreigners alike) without specific written permission to pass.
The trail leads off to the south (left) from under the bridge and up the Irkut.
The early part of the climb is easy. A couple hours of hiking brings you to a rock wall where the waterfalls begin. To your right a couple hundred meters below the first waterfall is the fork in the river that marks the usual camp area at about 1700 metres in elevation. The Irkut is the fork to the right, the Muguvek leads straight up towards Munku-Sardyk.
You follow the Muguvek up through the waterfall area, out through some high tundra shelves, all the while within the canyon of the Muguvek. This part of the hike is not particularly steep. Just below Lake Ekhoi (located at 2613 metres), you come across a section of steep bouldering before breaking out onto the lake shelf.
The lake is crossed in winter via the ice, in summer look for the best route. The route then continues up the south-west (right) side of the boulder field, making a beeline for the rocky outcroppings in the ridge below the summit block on the south side.
Once the ridge is attained, it is a brief ridgewalk to the east towards the pile of boulders that marks the summit block. Be careful of strong winds from Mongolia to the south that can easily throw you off the loose rock on the summit. The top is marked by a large Russian Orthodox cross and the fact that there is nothing even remotely as high anywhere around.
Crampons are an absolute necessity. Some people have climbed without an ice axe, but this is a dangerous situation due to the winds alone. It is very common for people to break off the slope on the return trip from the summit when descending the snow-covered glacier due to the hard crust on the ice that gives little purchase for cramp-ons. While death may not be imminent, serious injury is very possible.
Heavy clothing is essential. It's cold in the tents at night, and while it can be quite warm (two- to three-layer weather) during the day, a sudden storm will bring the temperatures back down to -30. Many people wear scarves over their faces or heavy creams to protect from snow glare and sever wind burn. Good sunglasses are essential. Some parents will rope their children to provide extra security. This is not a bad idea for inexperienced climbers.
Bring plenty of water in the winter on the summit attempt, and possibly a light-weight stove. In case of emergency snow and ice can be heated.
A four-season tent is a necessity unless it's the middle of July, and bring plenty of food! The walk to the camp spot isn't that far, and there are many beautiful mountains to see and climb in the area. You could easily spend several days.