To Expand on what fredP said-
Aircraft stability is directly tied to to relationship between three key points - aircraft center of mass, aircraft center of lift, and aircraft center of drag.
Generally when you're talking 'statically stable' (not specifying an axis), essentially what you are saying is that the airplane, if left too its own accord, will keep the pointy end pointed into the wind. Thus you are primarily talking about pitch and yaw.
The (slightly oversimplified) overview is that the aircraft's stability can be directly defined by the relative locations of the center of Drag and center of mass... if the center of mass is in front of the center of drag, the plane will be statically stable (like and arrow), if they're in the same place, it will have neutral stability, and if the center of drag is in front of the center of mass, the plane will be statically unstable.
Roll is another animal entirely, forget it for a moment.
The situation is a bit more complex than that - first off, while center of mass is (relatively) stable in the aircraft, the center of drag will change based on the aircraft's attitude with the oncoming air stream... To be 'truly' statically stable, the aircraft's center of drag must ALWAYS remain behind the center of mass regardless of the plane's attitude.
Furthermore, The above simplification applies almost directly to yaw, pitch stability is a slightly different matter, because- as a rule, pitch stability is a simple matter that the center of lift of the aircraft MUST be aligned precisely with the center of mass... if the center of lift moves behind the center of mass, the plane will nose down. If it moves in front of, it will nose up. This need for very precise alignment of these two points is why aircraft have trim mechanisms.
So to answer your question - want a plane with a little more yaw stability? increase the size of the vertical stabalizer... This will move the center of drag far backwards whenever the plane is off axis horizontally, and keep the fuselage in line with the airstream. Conversely, want a faster (less drag) more manuverable aircraft? shrink the vertical stabalizer, and the center of drag will be less effected by off-axis body movements, so there will be less of a tendency for the plane to want to 'right itself' back into the wind.
Pitch stability is similar but slightly more complicated. Giving the aircraft a good mechanism to finely trim its attitude so that the center of lift stays aligned with the center of mass is the first step. In general though - the horizontal stabalizer is much larger than the vertical stabalizer, so center of drag shifts based on pitch changes will be larger than with the rudder. The key thing to making a 'pitch stable' aircraft is sizing the elevators correctly so that the effect that they have on the center of lift is commessurate with the wing's lifting ability, such that it provides an 'intuitive feel' for the pilot... Or - in plane english - Make the horizontal stabalizer and elevator smaller, and the elevator's deflection will have less of an effect on the aircraft's center of lift, causing slower pitch movements ('lazy, stable in pitch'), make the elevator and horizontal stabalizer huge, and its motions will cause much greater changes in center of lift (because the horizontal eppenepage will exert greater forces relative to the aircraft's wing) and the plane will be very 'light' in pitch.
All of this and I haven't touched roll stability yet
There are two main mechanisms to achieve roll stability... one is the pendulum - I.E, keep the aircraft's center of gravity below the center of lift. The other is positive Dihedral - tilt the wings upward a bit causes the center of lift to shift from one side to the other in a bank (the Wing that is more perpendicular to the axis of gravity is using more of its lift force for lift than turning), hense the center of lift will shift towards the low wing, providing a force to re 'right' the aircraft. Its worth noting that center of lift starts to go a bit haywire in un-coordinated high roll angles - so very few aircraft will be roll stable past ~30 degrees of bank.
So - as an aircraft designer trying to tweak your roll stability - create a high wing plane with positive dihedral and... well, you have pretty severe overkill - but the combination of pendulum action and center of lift shifting will make an aircraft that doesn't like to turn (very positively stable). Create a low wing plane with negative dihedral, and you'll need to fight the whole time to keep the shiney end pointed upwards.
This is all ameteur understanding, based on reading books and discussions with my (PHD
in Aeronaughtical engineering) father.. I'm sure there are intracacies that I've missed, but for the most part I'm pretty confident in it.
Thus- want a _really_ roll-stable