Skill chance: at the Skill one can START making things, Tailor and most other crafting skills are 50% chance to make. Smith, on the other hand, is 0% at the "level to make".
Most skills increase at a 2/1 rate, once you get them (a few select items are different, and I think at least one crafting skill increases 5/2).
Chance to make exceptional, below 95 skill*: Chance to craft (without talisman) minus 60%. It is calculated internally even if you aren't up to 60% chance to craft yet.
* From 95-100, Exceptional crafting for at least Tailor & smith increases to 5/1 advancement (normal crafting chance stays at 2/1), and returns to 2/1 for skill advancement over 100, making the exceptional chance equal to Chance to craft - 45% for skills 100.1 to 120.0.
Normal Talisman Bonus: Adds to chance to craft, but only if one has reached the skill where one is able to make the item without a talisman (even if only 0.2%)
Exceptional Talisman Bonus: Adds to Exceptional chance, even if the displayed chance is 0% without the talisman. So, if one is 50% chance (without a talisman) to craft something, and you put on a talisman with 25% Exceptional chance, that will give you a (50%-60%+25% =) 15% chance of crafting the item exceptionally.
If a Talisman has both normal and exceptional bonuses, the normal bonus does NOT increase the exceptional bonus.