All you have to remember are the four main points of the compass. All the other points are made by combining these four. (for instance halfway between north and east is northeast).
Some silly ways to remember the order of the points are to recall the following phrases. The points start at the top and go around clockwise.
If you wish to quote a more accurate direction you can either opt for a more complicated compass point; North by Northeast is a position halfway between north and northeast. Note that the convention for naming points of this type is to quote the 'more important' compass point first. For example, halfway between southwest and west would be called West by Southwest (and not Southwest - West). or you can resort to quoting an angle measured clockwise from North (in degrees); Recall there are 360° in a circle. So North would be 0°. East would be 90°. South - 180° and West 270°. As another example, Northeast would be 45° (halfway between north and east). The advantage of quoting in degrees is speed and accuracy (a direction of 208° is not an obvious compass point!). This is related to bearings.