The Pradosham falling on June 30, 2008 is on a Monday and therefore it is known as Soma Pradosha and is considered highly auspicious. This is because Monday is dedicated to Lord Shiva.
Some Shiva devotees only fast during the Pradosham falling during the waning phase of moon.
The strictness of the fast depends on the devotee. The fast is broken in the evening after prayers.
The puja and worship is done in the evening.
The Pradosham period is in the evening from 1.5 hours before sunset and 1 hour after sunset. Most devotees make it a point to be present at a Shiva temple during this period.
(Please note that the three Pradosham in June 2008 is based on English calendar.)
More details about the fast, its benefits and myths regarding Pradosham can be found in this post – Importance of Pradosham.