I know that there are a lot of different types of media in the Fate series (tv, movie, light novel, video game, etc.), but I've never been able to figure out how interconnected they all are. I know that Fate/Zero (tv series) acts as a prequel to Fate/Stay Night (tv series), and I assume that the manga or visual novels with the same names share the same storylines, but beyond that, I have a hard time figuring out how they all connect.
Fate/Zero is the prequel to Fate/Stay Night, taking place 10 years before the latter. It originally consisted of 4 light novels written by Gen Urobuchi with the story set by Kinoko Nasu, who wrote the original visual novel. The former revolves around Kiritsugu Emiya and his involvement in the 4th Holy Grail War. The latter revolves around Emiya Shirou and his involvement with the 5th Holy Grail War.
Fate/Hollow Ataraxia is considered the sequel to Fate/Stay Night, taking place 6 months later. It's really half story-canon and half fandisk.
Fate/Extra takes places a long time after Fate/Stay Night, but in a parallel universe. It pushes some fun concepts and new servants and is for the most part considered a canonical part of the Nasuverse.
Fate/Kaleid Liner Prisma Illya started out as more of a gag-dojin manga serialized in Comp-Ace. It tells the "what-if" story of what would happen if Illya became a magical girl and had to capture Servants as cards. This series is not considered canon.
The Carnival Phantasm anime series was adapted from a gag-dojin manga called Take-Moon, published in Type-Moon Ace magazine and authored and illustrated by Eri Takenashi, who did Kannagi. It mostly revolves around inside jokes about Type-Moon and characters from other Type-Moon series, who end up meeting each other in the same universe for one reason or another. While this series is not considered canon, certain references are made to their respective canonical series.
Fate/Strange Fake is a short fan-made non-canon light novel written by Ryougo Narita, the writer of Baccano! It was was first released online as an April Fools' Day joke with no illustrations, but was later inserted into Vol. 2 of the Type-Moon Magazine. The story is set in Snowfield, a small town in California (north of Las Vegas, Nevada), ten years after Fate/Hollow Ataraxia, during an incomplete copy (with no Saber-class servant) of the 3rd Holy Grail War, supposedly initiated by the US Government.
Fate/Apocrypha was originally intended to be an online game, but the plans fell through. It later became a light novel series written by Yuichiro Higashide and illustrated by Ototsugu Konoe, with 3 volumes released at Comiket. The story is set in a parallel world (to the main Fate universe) in which the Grail was removed from Fuyuki City after the Third War, so the events of Fate/stay night and Fate/Zero never occurred. The story focuses on the clash between the two opposing factions, Red and Black, with each summoning 7 Servants of their own, and the Grail itself summoning special Ruler-class servant as a mediator of this Holy Grail War. Whether or not it's canon has not yet been determined.
Fate/Prototype is a reimagined version of Nasu Kinoko's original draft of Fate/Stay Night, which Nasu wrote during high school but which was eventually vastly overhauled to be a visual novel to be more suitable to target audiences. Much of the lore stayed the same, but the system of the Grail War differed. Though certain character archetypes and concepts (i.e., Gilgamesh, Avenger) stayed the same, the main character Ayaka Sajyou and her Servant are gender-swapped compared to the visual novel series. Though never officially stated, this series is probably non-canon.