Take Route 4 North from Rutland center and turn right onto Wheelerville Road. The turn from Route 4 to Wheelerville is at N43.64813 W72.90346 which is just after the road becomes 2 lanes at 50 MPH. If you make it to Pico you've missed your turn (two turns back). You stay on Wheelerville for close to 4 miles before reaching a sharp bend in the road with a turnoff to the left, this is the trail head. Please note that Wheelerville is an unpaved road.
This hike takes between 4 and 6 hours with ~2500' elevation gain. From the trailhead travel east on Bucklin trail. You'll cross over a stream via bridge at two points during your first 1.2 miles. Bridges were added at these crossing in the recent past. The trail remains flat for the first 1.9 miles then starts a increasing incline for the next mile. The trail merges at this point with the AT/LT and you'll bear right here continuing a short gradual climb for another quarter mile or so till you reach the Cooper Lodge. The intersection here is not well marked but take a 90 degree left at this point and you'll be on the Killington Peak spur trail which becomes a steep scramble once you pass the Cooper Lodge area tent platforms. Another .2 miles and you reach the peak . Return via the same route.
The majority of this route can be done in any comfortable footwear but if the rock on the peak spur is wet you'll need something grippy. For winter ascents use your common sense. Hiking poles will help you for half the trip but the bottom is virtually flat and the last section is too steep and boulder filled for them to be useful.