Red Pine Lake is located up Little Cottonwood Canyon, on the south side of the road. Parking at the trailhead can be a bit crowded during peak season (between June and September) so arrive early in the day for a good spot. The lake is a 3-4 mile hike up the trail, most of which is rather gradual. However the last mile or so is moderately difficult. 

AllTrails.com has a great detailed overview of the trail itself and the elevation gain involved. Check it out here! 

No fires or pets are allowed given that Little Cottonwood Canyon is considered Watershed. So plan on cooking with a backpacking stove/cooker.