Directional boards are most common with Freeride, Powder and All Mountain boards. Although you can ride them normal or switch, they are better suited to riding in one direction.
The bindings will be set further back, the board therefore having a longer front and shorter tail. The back of the board is stiffer than the front.
Like directional boards, directional twin boards will have the bindings set further back. However, the back of the board will have a softer flex than the directional boards.
All Mountain boards will commonly have a directional twin shape as it allows for good performance on groomed pistes, powder, and in the park.
True twin boards are symmetrical in shape, flex and binding position. This means performance is the same, whether they are ridden normal or switch. True twins are most common on freestyle/park boards.
A camber board will arc in the middle of the board. This allows for an even pressure along both the surface and edge of the board when the riders weight is added.
These boards are more suited to experienced park and groomed piste riders, as the shape provides more pop and 'energy'.
A rocker board will bend up at the tip and tail. Beginners will prefer a rocker bend as this will prevent you 'catching an edge' as easily as you do on a camber board.
Mixed bend boards are becoming more popular each year. There are many different variations being used by manufacturers, which can involve a 'wave' shape along the board. This bend tries to bring the best of both worlds together.
As a basic rule, if a snowboard stood on its end reaches between your chin and nose, it's a good fit. However, there are other factors to consider, for example, what type of riding you plan on doing? The riders weight also needs to be taken into consideration.
Heavier riders will want a longer board, and riders wanting to spend their time in the park will want a shorter board.
The width of a snowboard can be just as important as the length (thats what she said). The snowboard boot should overlap the width of the board by a small amount, but not so much as to touch the snow when carving an edge.
Unfortunately, there is no industry standard for how wide boards are, and even different boots with the same 'size' can have a different outer length. If in doubt, ask either in a shop or on a helpful forum.