From Tucson, drive straight east on Speedway Boulevard all the way to the end of the road. Park at the marked Douglas Springs Trailhead.
If you're looking for a long hike, this is it. It's 26 miles, with 7,435' of elevation gain to the top and back.
From the Douglas Springs Trailhead, it's a long ways up to the summit, but it's all trail. Start hiking on the Douglas Springs Trail as it heads east up the broad western slopes of Mica Mountain. As you get higher, you'll get some good views of Tucson and Rincon Peak to the south. The slopes are open and grassy at this point, but as you get higher, you'll enter the trees. After about 5.5 miles, you'll reach the Douglas Spring Camp. After 8 miles, you'll reach Cow Head Saddle at 6,100'. Continue east on the Cow Head Saddle Trail as it heads for Mica Mountain. On the way up, you'll pass by Helens Dome and Spud Rock. There are a maze of trails up here, but just follow the trail signs and they will guide you all the way to the rounded summit on top of a little knoll. There are no views here, but there is a sign marking the summit. You can hit Spud Rock on the way back and get some good views.