Steps in wand magic:

Break some branches from trees until you get the right one
Easy step once your aspects/staff magic are high enough to identify the rune of a branch

Find feathers until you get the right one (shooting birds, gathering feathers from the ground)
Easy step outside of specific feathers (vas-arn--phoenixes, silverfalcons, can be hard to gather)

The materials together are pretty heavy, you probably want a horse for a lot or rely heavily upon innrooms / lockers.
A horse allows you to be somewhat sociable while doing this.

Prepare a branch with the right feather:
Drains meaningful mana (a midbie can only prepare one branch before resting, beginner mage mentals might get two, super mage might get three)
This only trains "staff magic"
Has a relatively high chance of failure
(I'm not certain if failures train anything)

Engrave a mantra on the prepared branch
Drains ALL your remaining mana
Trains magic arts, staff magic, arcane runes, aspect runes
Has a relatively high chance of failure
(I'm not certain if failures train anything)

Using a wand:
doesn't train anything as far as I can tell.