You can start from the beach at Anse L'Ivrogne, located between the Pitons or dingy into Soufriere and take a taxi to the trailhead 600' up the mountain.
Start early as it gets hot once the sun swings around and bring plenty of water.
Be aware that the anchorage between the Pitons can be very rolly at times' I just slept on the floor the one time we tried it after almost getting thrown out of bed numerous times from the swell.

Drink all day at home, your friends worry about you; do it on vacation and they say "what a good time you're having". Save your friends needless worry, travel more!