"Everybody" is the first commercially available Madonna song, and the one who made Madonna began her successful music career.
In the year 1981 Madonna had just broke her contract with "Gotham Productions". She had recorded some songs for them with Steve Bray. She had worked for "Gotham" for one year, and then used this experience to keep on with her music work, but now with a greater power and control than before. So she kept writing songs with Bray, and some of the songs composed at that time are "Everybody", "Burning Up", "Stay" or "Ain't No Big Deal". Many years later, Bray would rescue those demos and recordings and released an album called "Pre-Madonna" (a.k.a. "In The Beggining").
Madonna liked dancing clubs and the night, and she often went to the most famous discos in New York, and met all the important dj's at that time. One of those was Mark Kamins, a dj from the "Danceteria" disco, and would become a friend of Madonna. Kamins was beginning to produce songs, and accepted to hear some demos Madonna had recorded with Bray, and when he decided to play them in the disco, he could see the great acceptance of the people. Then he talked with Michael Rosenblatt, an executive from a growing record company called "Sire Records", part of "Warner Bross". So, in a little time, Madonna had her great chance in front of her: a contract to record three singles, three dance tunes, and she would receive $5'000. As a curiosity, Madonna had to go to the hospital where Seymour Stein ("Sire"'s president) was recovering from some medical treatment in order to sign the contract.
Two songs were chosen to be the first Madonna release as a single: "Ain't No Big Deal" and "Everybody". People at "Sire" didn't like the first one after being recorded in a studio, and they rejected it. A few years later that version of "Ain't No Big Deal" was released as the B-side of "Papa Don't Preach". So "Everybody" was the song in both sides of Madonna's first single release. Bray was supposed to produce the song, but people at "Sire" and Madonna saw that he hadn't experience enough and choose Kamins to produce the single. This decision led to a great argument between Madonna and Bray, and they even didn't spoke to each other for a long time.
"Everybody" was officially premiered in the "Danceteria" disco, where Madonna performed it lyp-synched in front of "Sire" and "Warner" managers. Madonna had made a choreography for the tune, with three dancers, and taking care of all the performance skills, which pleased the managers, and they saw that Madonna had a great potential.
"Everybody" didn't have success in the beginning, althoug it sold a great quantity of 80000 copies in the first months. People thought Madonna was a black singer, a fact supported by her not appearing in the single cover, and the rhythm and blues radio stations where the ones which aired the single most. The managers of Sire were so secure of the success of "Everybody" that they decided to release a video for the song, something really exceptional for that time. The video wasn't very good, well, but it really helped to promote the single.
Although the hit was successful in the US, the idea of releasing it in other countries wasn't as good. For example, in UK, "Warner" considered that this song was created for a very specific market. But some promos and singles were released for UK and Italy, and are hard to find for the actual Madonna collectors.
Talking about the song itself, it is just a dancefloor tune, with a catchy chorus encouraging people to dance, probably too pretentious and not catchy enough. A hardly syntetized beginning leads us to an spoken intro and a direct invitation to get up, dance and sing. The lyrics show the way of thinking of Madonna, very optimistic, and in this her first song, she begins to let the people know what she wants: Dance and sing, get up, and do your thing...

"Everybody" is the first oficial single from Madonna in "Sire Records". But by 1982 Madonna had recorded lost of demos and studio recordings.
The first serious contact Madonna had with music was in 1979, when she became part of the "Breakfast Club", with her boyfriend Dan Gilroy and some other members, and she played drums. Then, Madonna would take part in many different projects: she sang background vocals for Patrick Hernandez and Otto Von Wernherr, and she even played the role of Bruna in the film "A Certain Sacrifice". In 1980 she joins another band, "Emmy And The Emmys" (a.k.a. "Emmy"), and they recorded several demos and even performed live in some concerts. In 1981 she got her first manager to direct, not very successfully, her musical career as a solo singer. There are many recordings of songs from that period sung by Madonna, some of them with good quality, that can be found quite easily in the internet or in some bootleg cd's.

As this is one of her first songs, we can't exactly say all the times she performed "Everybody" live. In most of them, Madonna appeared in the stage with two or three dancers: her brother Christopher, designer Erica Bells, and Bags. Here you have a complete guide to the most famous performances of this song:

In 1981, Madonna performed for the first time an early versión of "Everybody", many years later rescued by S. Bray in the "Pre-Madonna" album, in the "Danceteria" disco.

We can say that this is one of the first Madonna solo concerts, it took place on September 24th 1983, in "Uncle Sams", and she performed live "Everybody" and other three songs from her first album: "Madonna".

She also performed in the famous "Roxy Night Club" in 1983, where she sang "Everybody" and "Physical Attraction".

In the TV, one of her first performances was this one in the "Dance Party" tv programme, in the US.

She also made this performance in the italian television show "Di Gei?" in 1983.

And the best performances of "Everybody" were in her tours. "Everybody" was part of the list of songs from her first tour: "The Virgin Tour".

The last time Madonna has performed live "Everybody" was in her world tour "The Girlie Show" in 1993. This song was the last song of the show, and she mixed it with S.Stewart's "Everybody Is A Star".