As you exit Saint Jean Pied de Port through the old arch, take the left fork in the road at the intersection and just walk UP!
Follow either the red over white stripe GR 65 postings, or the yellow arrows. If you come to a fork in the road, you generally take the one that goes UP...usually left..but this IS France...(sic)
At about 8 km you will come to Refuge Orisson. You cannot really miss it as it is the only substantial stone two-story building in sight. It is on the right about 1 km AFTER the Hunto albergue.
The typical walking time is about 2.5 - 3 hours from St. Jean. However, and as they assign even reserved bunks on a FIFO basis, arriving earlier rather than later is better.
Besides, on a clear day, the panoramic views from the deck across the road are stupendous! Admiring the view, while meeting new friends and sampling the local vin rouge (you are still in France), while working on your sun tan, is not at all a bad way to cap off your first day. If you arrive much after noon - 13:00, you might find yourself assigned to a less desirable bunk room or even the overflow tents out back.
Bear in mind that the climb from St. Jean to Orisson is the steepest incline over the ENTIRE
Camino Frances. It is only 8 km, about 5 miles, but it IS quite steep. This said, there will be others walking, and huffing and puffing along side you.
Later on, after you are more acclimated, there will higher climbs and longer ascents, but none is as steep as that first bit.
To be truthful, there IS a 12% grade just as you cross into the province of Palencia, but that is a long, steady 1 km climb, and you have been walking for two to three weeks already, so you should not be daunted. Just keep this in its context and you will be fine.
I hope this helps.