The best way to get to Catalina is by helicopter or small plane there are many services available out of Newport and Long Beach (90 minutes N of San Diego). However us regular folk travel by boat, they leave from the same cities and take between 45 and 60 minutes to get to Avalon.
Once you get to Avalon you have a number of choice hotels, restaurants, dive shops, and campsites to choose from (most are on the web). Try to spend at least two days, you will enjoy it.
This is a toughy, there are several places to shore dive on Santa Catalina, and several dive boats that leave at un-civilized times in the morning, I prefer to eat my breakfast and catch a later boat - gives me time for a quick shore dive too! The shore diving primarily centers around the dive park in front of the Casino, ask at the local dive shops for other sites. The entry at Casino is over a low (3') wall and across a large number of big slimy (ankle spraining) breakwater rocks. They have been threatening to build a series of steps into the water, and most of us just can't wait (They have built this entry now, and the line in and out is something to see -ed). This might not be the spot to bring ALL of your new camera gear (I'm speaking from experience here), but an old camera and flash can be handled just fine. Before you finish your gear-up, watch the other divers coming in and going out, time your entry to take advantage of a lull in traffic, take it slow, and you will have a great dive.
Everybody in the dive park is protected, and they know it! You'll see lots of Garibaldi (surprised?), schooling fish, Sheepshead, and Rays. They have 5 wrecks and lots of kelp within the park, so the fish love the area.
One word, STEEP. You can easily get down to 110' on a shore dive, in fact the wreck of the Suejac rests on the seafloor and is at 40' at the stern and 100' at the bow. Otherwise, lots of kelp, large rocks, and small sandy areas, dropping off consistently from the coast out.
Usually very calm, this is the protected side of the Island. Visibility hovers around 40 feet and water temperatures usually run a few degrees cooler than the coast (50 winter, 60 summer)
Large slick rocks along the Casino, take your time getting in and out. The extreme slope of sea floor, and the clarity of the water (compared to the coast) means that you can be deeper than you might expect so keep an eye on your depth gauge.