How would these decisions have been propagated throughout Europe. Would copies of their decisions been sent to every church? Would copies be sent to the bishops and gone out from there by word of mouth?
Four hundred odd bishops attended the council in person. This is about half the bishops in Europe. So most of the bishops would know about the decrees of the council because they were there. Many of those bishops that didn't attend in person probably sent a representative. The remaining bishops would probably be informed about what happened by their archbishop, or by a neighbor.
The bishops would call meetings of their local parish priests to propagate the decrees of the council (or possibly he would delegate the job to one of his officials; say an archdeacon or dean). The bishops would have written copies of the decrees; they would have scribes make copies of these as required. Individual priests would generally be unlikely to have a copy of the decrees (I think); unless they are some sort of canon law specialist. But normal priests would have easy access to a copy of the decrees at the bishop's court, and possibly elsewhere.
See http://www.newadvent.org/cathen/09018a.htm
Note, that the fourth Lateran council wasn't really a "decision making" body. The council was largely there to listen to (and sagely agree with) the decisions that the pope (and his advisers) had already made.