Sailor Moon is about an ordinary, klutzy, crybaby, 14 year old junior high school girl who receives a special quest from a talking cat named Luna to fight evil and find someone called the "Moon Princess". She accomplishes all this by transforming into the sailor suited "pretty soldier" Sailor Moon. Over time, she discovers other Sailor Scouts/Senshi and another cat Artemis who join her as a team.
She also runs into this cute guy named Mamoru/Darien and this caped hero Tuxedo Kamen/Tuxedo Mask. Coincidentally enough, they happen to be one and the same. Tuxedo Kamen/Tuxedo Mask reappears constantly to save the Sailor Senshi/Scouts from the generals of the Dark Kingdom/Negaverse who, at first, begin stealing life energy out of people, then attempt to acquire the ginzuishou/Imperium Silver Crystal. Then Sailor Moon learns about the Silver Millenium/Moon Kingdom.
The Moon Kingdom was what existed a thousand years ago when the universe was at peace. It was ruled by Queen Serenity, until the evil forces from the Dark Kingdom/Negaverse decided to try and take over. Queen Serenity was able to repel the invasion, but only by sacrificing herself and sending all of her court and the ginzuishou/Imperium Silver Crystal to the future on Earth.
Now, all this ties into the plot because Sailor Moon a.k.a. Usagi/Serena just *happens* to be a reincarnation of the Moon Princess, Princess Serenity/Princess Serena in addition to just being Sailor Moon. It also turns out that the Sailor Senshi/Scouts are reincarnations of the guardians of the Moon Kingdom, and that Mamoru/Darien is a reincarnation of Prince Endymion/Prince Darien, who was to marry Princess Serenity/Princess Serena. This adds a bit of romance to the series, but in the end, the Sailor Senshi/Scouts and Tuxedo Kamen/Tuxedo Mask are able to use the ginzuishou/Imperium Silver Crystal to *annhilate* the Dark Kingdom/Negaverse, but at the cost of their own lives.
Note: In the DIC translation, no one dies. Everyone just has their memories erased. Reportedly, the original makers of the series weren't sure if they were going to do a second season, and so they wanted to potentially end off the series with a bang. The way this works in the original is that the Sailor Senshi die, but their alter-ego secret identities live on to have a chance at a normal life.
Introduction to the Sailor Moon R series
Anyhow, the next season of the show starts, and everyone gets their memories restored, except for Darien/Mamoru (to the annoyance of Usagi/Serena). Two aliens, Alan/Ail and Ann arrive on Earth and start stealing people's life energy for a tree called "Doom Tree." At the end of the saga we find out Moonlight Knight (Who is Darien) is the split personality of Darien because he didn't get his memory back Moonlight Knight was sent to help Sailor Moon. Serena revives the Doom Tree by using her crystal and alls well.
Just when things start to get comfortable, all of a sudden a strange kid who looks an awful lot like Usagi/Serena falls out of the sky with a quest to find her mother and the ginzuishou/Imperium Silver Crystal. She's Chibi Usa/Rini, and she's from the future, but she didn't come alone. She's followed by some agents of the Black Moon/Negaverse(again!), namely Rubeus, and the four weird sisters, Cooan/Catsy, Beruche/Berti, Petz/Avery, and Karaberas/Prisma. In an interesting change from the usual, the Sailor Senshi/Scouts were able to heal the sisters of their evil rather than just kill them like usual.