Eruption Times
In the beginning of an eruption, the authorities close access to the volcano, while experts map out the situation. Then, they generally open access to certain areas. Follow the instructions. It is probably much easier with a local person.
Eruption are a major attraction. Expect traffic jams.
Coastal Road
It is impossible to climb from the seashore onto the volcano - there are no paths or trails, the volcanic rocks are difficult, fog may set in, etc., so the only access is through the Pas de Bellecombe.
However, driving on the N2 coastal road at the bottom of the volcano is very interesting. The road cuts across volcano rock. Sometimes this rock is fresh - occasionnally, erupting lava will cut across the road. The highway services then rebuild the road on top of the new rock and signpost the year of the eruption.
Into The Caldera
You must have a car, though some group tours may be available.
The N3 route des plaines "road of the plains" cuts a diagonal in the island, from Le Tampon to the eastern shore. A clearly signposted road forks off from it and goes in the direction of the volcano le volcan and the pas de Bellecombe. After a few kilometers the local road becomes a well-maintained forestry road, and in the final kilometers it becomes a well-maintained track.
Park your car at the parking lot at the Pas de Bellecombe.
It is better to arrive early in the morning, for mid-day fog will set in. Remember that the northwestern coastal roads are frequently jammed, and that the route des plaines and the volcano road are mountain roads, so it may take a while to drive there from Saint Denis.