Which is smaller potassium or potassium ion? Why?

The potassium ion is much smaller.  

As the atom loses it's electron (simple answer) it's net charge
becomes positive.  This unbalance causes the negative electrons to be
pulled in closer to the positive protons, because each proton now has
a slightly greater pull on the electrons.

The complicated answer isn't something they teach in first year
chemistry, so I dont' know what it.

The cation for potassium is smaller because of the loss of a higher
energy valence electron.  The potassium atom has electron
configuration of [Ar] 4s1 where as the potassium ion has the electron
configuration of [Ar].  The fewer number of electrons allows for less
shielding and a greater amount of attraction to the nucleus of the
atom.  The giving up of electrons/cations create smaller radii than
the normal atoms while the atomic radii of anions is larger than the
ground state atom because of more shielding and less 'pull' from the
nucleus.