To train horses, you need a saddle, an appropriate horse (which, if my poor memory serves can be an untrained _____), and some Horse Rearing skill. The better your skill, the better chance of success you have. You have to go to the Horse Farm (not far from Uxhal), and use the open stable door near the Horse Master.
The following are useful for you for some of the various craft skills:
Mining: (some sort of) pickaxe & access to a mine (marked on map).
Smelting: coal, tin, copper, iron, etc (from mine).
Metalwork: bronze/iron/steel bars & tools.
Woodcutting (some sort of) hand axe & access to a wood (marked on map)
Fletching: wood (of various sorts) & tools.
Leatherworking: tannin, furs & leathers (the latter two can be acquired by hunting)
As a general rule, the crafting system will only list options that are available at your skill level. For example, if you're not very good at metallury, you'll only be able to make simple knives rather than that broadsword you had your eye on.
Basic items tend to be created in one go (knives, for instance). More complex items need to be assembled from components. For example, creating a lance requires a lance head (metallurgy) and a wooden pole (fletching). Once you've got both, you can assemble the item from pretty much any crafting screen, by choosing what you're trying to make and checking you've got the parts.
A quick note by way of example:
- bows require just wood
- compound bows require wood & horn
- crossbows require wood & a loading mechanism (winch, etc, etc).
You can always try to assemble an item you don't have all the parts for to see what it requires.