i feel dumb, but how do i train manufacturing skills

I'll use Blacksmith as an example.
Go to a blacksmith and select 'manufacture weapons'. Now select a weapon to make. When you have the materials shown on screen, press start and your weapon will be made. Upon completion, you'll receive 10% exp to your blacksmith skill. When you've made 10 weapons (thus reaching 100%), go to an Elder, select "Learn manufacturing skill" and upgrade the skill to its next level.

Amiris's Post does work off the assumption (not necessarily wrong) that you have done the quests at level 5 to actually have the skills at level 1.
Please also note 2 points ..... #1 all Manufacturing starts at level 2 (level 1 craft req), only finished Products give progress (some processes like crafting ammo don't give craft experiance). #2 Make certain you have the materials the process takes (this might seem obvious but it is the most common mistake).


further note; advancement requires 10 crafts (10% per), translated: to advance level 1 - 2 (10 level 2 items), level 2 - 3 (after visiting elder to learn level 2, 10 level 3 items). Finally craft level 4 can only be learned by completing a quest available at level 50.