Carving
    Wood carving is a trade skill.  You learn carving no matter what you carve.  So if you are trying to make weapons, you basically learn carving plus a little bit of weaponsmithing.  Or if you make arrows you learn carving plus a bit of bowyering! 
      So now how do you do it and what can you make?  Well thanks to the help of Gorm, I will tell you a bit about it....
     First you must forage branches to carve. You  just forage (wood type) branch in the propar wooded area
    The available woods are... cedar, cherrywood, driftwood, fir, maple, mahogany, oak, pine, spruce, teak and willow.
     The current skills you can learn from carving are:  Armorsmithing: making bracers and a shield
Bowyering: making arrows
Weaponsmithing: cane,club,dagger,staff & sword

Other things that teach general carving: anklet, box, bowl, bracelet, clogs, cross, necklace, pipe, ring, sheath, statue,  various animal toys, and vials
    The toys you can make are: bat, bear, cow, dog, dove, dragon, eagle, elephant, ferret, fox, frog, griffin, gryfalcon, hawk, horse, jackal, jaguar, kitten, lion, lynx, monkey, mouse, nightingale, owl,  panther, phoenix, rabbit, ram, rat, shark, snake, spider, stag, swan, tiger, turtle,  unicorn, whale, wolf, and wolverine.
     As you can see these are in alphabetical order.  Not in the order of skill required to make them.  So you need to experiment to find out what to do first.  I can tell you that vials are one of the easiest.... then staffs, boxes, snakes, bracelets and it goes up from there.  As with everything else, have fun!