The intersection with the Upper Manitou Incline Trail will happen first. If you chose to begin your hike via the Manitou Incline this is where you should meet up with the Barr trail. Just before this intersection the trail passes through a natural tunnel created by some very large boulders.
This sign marks the actual intersection. If you're coming from the Manitou Incline it will be hard to see.
Shortly after passing the Manitou Incline Trail you will reach No-Name Creek. This is the only reliable source of water on the trail until Barr Camp. If you are carrying minimal water and filtering you will want to stop here and top up, it's a long dry trail to Barr Camp.
Before the trail crosses No-Name creek there will be another trail intersection with this sign. If you're not in a hurry this is a fun historic area to explore. If you are taking multiple days to ascend the Barr Trail, some people choose to camp here.