When leaving the airport follow the road that goes straight on and then bends to the left making a turn around the airport runway.
Keep following the main road that winds through some villages.
After the village of Calibishie (around 15 minutes) you go up into the rainforest and after 10+ minutes you have to pay attention:

You reach a junction. One road goes straight/left uphill. The other 90 degree right down to the flat. Take the road that goes with a 90 degree angle over the bridge. (So not straight/left uphill but down to the flat)
Then continue to follow the winding road until you are in Portsmouth and pass the big sports field on your right hand side.

There, 50 meters after the sports field, at the T-crossing you take a left.
You will cross a bridge and see a gasoline station on the left. After the gas station you will pass 2 side-streets on you left.
After those the main road turns sharply left and UP (do not go straight towards the small port).
Follow the road until going uphill and bending right. When going downhill you will go over Picard River bridge. Keep driving straight passing IGA and the Medical Campus on your right. Keep going straight till you see a sign saying "Portsmouth Beach Hotel" on your right. Turn into their driveway and park at their parking lot. You are there!