Information on specific crafts can be found in the links at the bottom. There are general principles that apply to all crafting though.
Core character attributes (Might, Vitality, Perception, Willpower, Social, Agility) do not affect crafting. Crafting performance comes from skill ranks, perks, gear (Control, CP bonus, and Craftsmanship from enhancements and item stats), and which actions you use.
Dedicated crafting equipment still matters: it adds Control, CP, and Craftsmanship through enhancements and base stats on the items themselves. The SWLOR Design Bible has a particular page on Equipment - Crafting for crafters who want the best. If you're not a Smith, consult the Design Bible to find the best gear for you and commission a Smith to make it. In the meantime, do all the quests you can for your particular Craft Guildmaster to raise your Shop Level, since each Guildmaster sells non-enhanced dedicated crafting gear. Wearing that gear still improves your crafting numbers.
For top end crafting, build or commission a T4 or T5 weapon with two crafting enhancements on it (if you doublewield, commission two for even more bonus).
For a specific step-by-step example of how a Smith can build their first crafting gear, take a look at Epiphany's Guide to Building Smithing Gear.
All crafting is driven by three values:
Every crafter should take Waste Not, Master's Mend and the Basic Touch perk. They're used per the Crafting Loop section below.
It is the collective agreement of every crafter interviewed that no other perk is worthwhile. Save your SP for the recipes.
If you're making something without enhancements, your loop is this:
Waste Not
Basic Synthesis x 4
Waste Not
Basic Synthesis x4
Master's Mend
Repeat until your progress is done.
If you're making something with enhancements, your loop is this:
Waste Not
Basic Touch x 4
Waste Not
Basic Touch x4
Master's Mend
Repeat until you've maxed quality. Then do the first loop until you've completed progress.
More specific information on particular crafting can be found in the following links:
Epiphany’s guide — building smithing / crafting gear (guild rank, T4/T5, enhancements, sample rotation)