Due to the volcanic nature of the island there are beaches with 2 different kinds of sand or pebbles; black and yellow. Black is far hotter on the feet! Bring your rubber sandals or flip flops or buy some here!
All beaches are accessible by bus. Red beach doesn't have red sand, its the cliffs behind the beach which are reddish that give it its name. Beaches are kind of boring on Santorini, the water is clean. Most beaches are long but you cant see into the waters for any depth, I guess because of the black sand shallows. The idea of a nice walk on the beach is always appealing but please leave behind the umbrellas and other trappings of commercialism.
Anyway, if with companion, I prefer a pool on the cliffs at my traditional apartment-plex, not because I am a snob but because of the views and ambiance. Its quiet, the views are incredible. If you can afford it DO IT! Greece has plenty of other islands with amazing beaches. Once you have seen one black sand beach, you have seen them all! What I am saying is: sure go to the beach but don't come to Santorini for the beaches come for the view!
Once at the beach, the ubiquitous beach umbrellas and beach chairs are rented by the hour by enterprising licensed Greek entrepreneurs. Well worth it and inexpensive. It is very, very, hot! Flip-flops mandatory!!
Karterados has a quiet black-sand beach and is closest to Fira.
Kamares (right) and Avis Beach: 5 km of black pebbles, not sand. Wading is difficult. It has clubs at night and water sports during the day. This is a very built up area and the most popular beach.
Perissa Beach: second most popular beach, farther away, more casual, black sand, extremely hot. It has tavernas, water sports, clubs at night.
Akrotiri Red Beach is smaller with yellow sand. It's quieter and there's a nude area at the end. It's more isolated and a short trek after the bus stops, nevertheless, it gets crowded. It's small and the shore is rocky in spots. Visit the dig then the beach. I don't know what all the fuss is about as a beach except you can take your clothes off due to its isolation.
Tip: Monolithos Beach: is where the locals go, wider, sandier, less expensive food. Yellow sand. ;)
Perivolos, Aghios Georgos Beach are quieter but with facilities for water sports, rooms to let, bars and tavernas. Vlihada Beach near Perivolos is quiet and nice!
Ammoudi Beach is situated directly below Oia: 214 steps below it, to be exact. There are a few charming houses and the old Venetian castle protects you from pirates.
Armeni Beach is 286 steps also below, with a tavern and occasional volcanic pumice floating on the water; a great free gift or souvenir also good for keeping feet soft.
Baxedes Beach is shady beach 3 km from Oia with coarse blackish sand and few crowds. It's on the bus route from Oia.
Here's a nice map of the major beach areas.