You are confusing the Horcrux with some kind of 'one-shot' or invokable magical talisman. Its function is not triggered by death, but rather its existence precludes death.
In general, for a person to die and their spirit to move on, it must ALL move on; the Horcrux functions by holding a portion of their soul in a safe, earthbound container. Until it is destroyed (destroying or freeing the soul) the person who created it cannot die in a permanent sense.
To quote Slughorn:
"Well, you split your soul, you see, and hide part of it in an object outside the body. Then, even if one's body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form... few would want it, Tom, very few. Death would be preferable."
The number of them was not meant to give Voldemort seven tries, as much as to make it that much less likely that all of them could be found and/or destroyed.
The Horcrux also does not provide the creator with a new body or any way to return to life.. its existence simply prevents the creator from being able to truly die -- coming back to life is the creator's problem.
Incidentally, it's not a new idea, having been seen in Mythology (
Koschei the Deathless, for example), Dungeons & Dragons (a '
Phylactery') and other sources. Its method of functioning varies; sometimes it keeps the owner from dying by rendering their physical form 'unkillable', in others it recreates the body after it is destroyed. Sometimes it simply keeps death from being final by holding the soul, as is the case with HP.
See this TvTropes link (warning; you can lose hours on TvTropes) for a list of examples.