Well, basically, Sandy, the sedevaticanists reject Vatican II because they see it as being "too liberal". They equate the liturgical nonsense, the awful music, the dissident clergy, and all the other problems in the Church with the council. Actually, Vatican Council II had nothing to do with these problems (which, finally, are starting to turn around); the silliness which Catholics have had to endure for the last 40 years have been the fault of liberal clergy and laypeople in Western countries. Vatican II actually changed very little in the practice of the Church---but the "liturgical reformers" haven't been putting Vatican II into practice; instead, they've been putting their own agendas into practice
in the name of Vatican II. (For a very good examination of this phenominon, read
What Went Wrong With Vatican II, by Ralph McInerny, Sophia Press, ISBN 0-918477-79-4.)
The sedevaticanists saw all this silliness that took place in the wake of the council, and they decided that it had to be the
fault of the council. And it naturally followed that since it was the fault of the council, why then, the council just
had to be the work of the devil. (Thus the references to "the smoke of Satan has entered the sanctuary", and all that kind of hogwash.)
Usually the sedevaticanists, since they reject Vatican II, will insist that only the Tridentine Latin Mass established after the Council of Trent is the only "valid" Mass, along with all the other reforms enacted by Trent; they want a return to what they consider to be the "glory days" of the Church, say about 1957 or so. Anything after that is anathema. They feel that Pope John XXIII, since he called the 2nd Vatican Council, was at fault for the disintegration of the Church, or rather, of their idealized concept of it. Pope John obviously had to be under the influence of Old Scratch hisself, and since the council was invalid, everyhting since then has also been invalid. The Novus Ordo Mass of Pope Paul VI is invalid, and Popes Paul VI, John Paul I, and John Paul II are also all invalid. In their view, the Holy See has been vacant ever since the last "real" Pope, Pius XII, died in 1958.
There are various shades of sedevaticanism; probably some of the most radical ones are the tiny group of loons who elected their own "Pope" in a clapboard cabin up in Montana a few years ago. (It makes you wonder if they were in cahoots with the Unabomber, two clapboard cabins up the road.)
The group with the most exposure is the so-called "Priestly Society of St. Pius X", a splinter group started by the late Swiss Archbishop Marcel LeFebvre, which is in open schism with Rome.
Archbishop LeFebvre originally seemed to have few objections to Vatican II, but as time went on, he became more and more distant from the authority of the Holy See, and by the early 1970s was an open dissident to Rome. On June 30, 1988, he "ordained" four priests of his movement as "bishops", after the Holy See had specifically warned him that he had no authority to do so without proper permission from the Holy See, and that if he did it anyway, he would suffer automatic excommunication with the Roman Catholic Church. He went ahead and did it anyway, and was automatically excommunicated, along with his organization and all his followers. Of course, since SSPX rejects the authority of Rome and the Holy Father, they shrugged this off as irrelevant. In their eyes, they are correct, and Rome is wrong, and they have attracted all manner of disgruntled conservatives and reactionaries since. They remain in a state of open rebellion against Rome, even though Rome has tried to reconcile the group many times since. Archbishop LeFebvre ended his days as a very bitter man, and his schismatic group is the fruit of his labors.
Anyway, that's a thumbnail sketch of sedevaticanism and SSPX. Does this help?
Blessings,
---Wols.