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-east (left) side of the boulder field, heading straight for the rocky ridge to the left and north of the summit block..
The ridge itself requires technical rock climbing and ice screws in the winter. It is considerably longer than the 1A route, and approaches the summit from the north.
I have not done this route, so I cannot provide more detail.
Crampons and an ice axe are an absolute necessity for the snow and river work. 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 imminant, serious injusy is very possible.
This route also requires standard climbing gear: ropes, helmets, carabiners, webbing, rock anchors and screws.
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.