For Avalon Dive Park (which is quite fun), you need to take the ferry to the island. It's doable as a day trip but the appropriate 6 am boat is early.
For most other sites (Catalina, Channel Islands, Rigs, etc.), you are better off a boat from the mainland. Although there are "open" boats (Spectre at all times, others on occasion), most local boats are charters booked by local dive shops, so you book through them. There are a bunch, with Eco being the largest, but there are also bookings by In2Deep, Zen, Ocean Safari, Divers-West and a few others. There isn't really a great index of all trips going out on a given weekend. Just look at the dive shop sites.