When planing the end grain of a piece of wood, a block plane is usually used.  However, planing end grain is a bit trickier than just knowing which type of plane to use.  Planing end grain has the added problem of part of the wood chipping off in the corner.  This is caused from the sole sliding off the edge of the wood and the blade digging in.  There are two ways to correct for this, either planing towards the center of the piece of wood, or adding a support.

Planing towards the center can be as simple as starting at the edge and planing towards the center, then doing that for the other side.  While being very easy to setup, this method can easily lead to a lower quality of workmanship.  Because you are using two different starting points, it becomes very difficult to keep the edge flat.

Adding a support is generally considered to be the better of the two solutions. It works by adding a scrap piece of wood to the end of the piece you are trying to plane.  This extra piece of wood will support the sole of the plane when you reach the end of the piece you're working on, and keep it from chipping.  In order to set this up you must first clamp the scrap piece of wood to the piece you're working on.  It is important that you line up the edges of the piece of wood you're working on and the scrap piece so that you do not accidently get flaws at the end of the piece you're working on due to a sole that is in the wrong place.  However, once this is done, it is much easier to come out with a good quality edge.