For the most part, walks in Zion begin or are centered close to the bottom of the canyon; the overlook walk is different in that one is hiking close to the top. As in other shorter walks, it is more of a stroll than anything else . . . as long as you don't mind heights.
To get to the start of this particular trail, one takes Route 9 into a tunnel carved right through the heart of Zion. The tunnel is old and narrow, and park rangers are on hand to supervise intervals of one-way traffic.
Very close to the exit of the tunnel is the car park (not to mention the ranger hut) for the start of the trail.
The car park is exceedingly scenic but not particularly large (although there are additional turnoffs for parking along the road), so as with most everything else in Zion, the earlier you do it, the better off you are.
From here, you have a choice of four directions: