Hi Alex J.,
A half-reaction is just a "theoretical piece" of your total reaction here. It shows just one of the elemental species (which can be the metal, or nonmetal, or oxyanions of them, etc.) being reduced or oxidized (you can show it either direction, tables of these always show them in a standard direction, oxidation I think). So, for example,
Cu+2 + 2 e- = 2 Cu0 which you could also write just as well, as:
(1/2) Cu+2 + e- = Cu0 ----- because the oxidation or reduction reaction doesn't care how much stuff is reacting, the electrode potential is an intensive quantity!
These are shown in the reduction direction, just switch the two sides around for the oxidation direction.
In some cases, half-reactions also include water being split to provide/consume H+, or O for/from complex species formation/destruction. Just sayin'.
I'll leave it to you to discover the other, similar "piece" for K . Then, to balance the total reaction, you just need to scale up each "half-reaction" as needed until the two pieces match in terms of electrons produced and consumed respectively. Here, it's easy to see that twice as much K (on a molar basis) is needed as Cu, since each K is only half as effective about producing electrons (one for K, two for Cu->Cu+2 ).
-- Cheers, --Mr. d.