Take the Cle Elum exit on Interstate 90 and head into town. Continue west through town towards Cle Elum Lake. Stay on this main road through Roslyn and a couple more small settlements before reaching Cle Elum Lake. Stay on the main road and at the headwaters of Cle Elum Lake, you will pass Red Mountain Campground. Continue on this main road another 1.3 miles where you turn off the main road onto Cooper Lake Road. Note your mileage here (all distances further will be measured from this point), cross the bridge over the river, and stay on this main road for 3.6 miles. At this point turn right onto gravel road 4613. 4613 switchbacks up the mountain a few times and then straightens out. At 5.6 miles from the main Cle Elum road, there is a smaller gravel road on your left that is a sharp 150 degree turn back to your left. Take this road and at 6.6 miles stay right, at 7.1 miles cross over a no name creek and then just beyond this at 7.2 miles there is an old abandoned road on the right. This is the trailhead, elevation 4,200 ft. I pulled a little ways onto this abandoned road and parked. There is parking for 2-3 cars here.
From the parking area, head south up the abandoned road. This old road has been disabled by the forest service and traverses an old logging site. There are ditches dug all the way across the road and all the culverts have been removed. Following the road south, you have to cross many ditches across the road and the piles of dirt on either side of the ditches. I counted 35 of these ditches you have to cross. The road goes south for about ¾ of a mile before it curls around the head of the valley and then heads northeast. About 1.25 miles from the trailhead (elevation 4,800 ft) there is a fork in the road. Take the right fork and climb up on top of a little ridge where the road ends. From this point to the summit, there is no trail.
Once you reach the end of the road, go east directly toward the summit of Red Mountain. The first part of this ridge is a brushy logged over area and then you reach the upper edge of the logging activity and the slope becomes much steeper. Climb this slope, staying mainly in the forested areas to the left and off the talus slope. I found some animal trails that helped me pick a route, but the main direction here is up and east to the summit ridge. This slope is kind of steep gaining about 800 ft in ¼ mile from the end of the road.
Reaching the top of the slope is not the end of the hike. The ridgeline is rocky and not very wide. Turn left(north) and climb the first highpoint that you see. I think this south highpoint is about 10 ft higher than the north highpoint, but you should still follow the rugged trail along the ridgeline north about 700 ft to the north summit. Return the same way you ascended. This total hike was 4.25 miles, gained about 1,800 ft, and took just under 3 hours.
The 10 essentials are always required. There is water along the old abandoned road in little creeks if you want to use that resource. A GPS may be handy depending on your navigation skills.