These rules cover all non weapon proficiencies except those relating to languages, which are covered by a different set of rules. I use competence levels and modified skill rolls, rather than the rules in the PHB. If you have a problem or need clarification on how these rules would be applied to a specific proficiency - Please talk to me.
Skill Levels
When a character spends 1 slot to learn a proficiency they are regarded as having BASIC skills in that proficiency. When 2 slots are spent the character is COMPETENT in that proficiency and when 3 slots are spent he or she is considered to be a MASTER craftsman.
Characters with BASIC skills can automatically perform the most basic skills associated with the proficiency. BASIC swimmers can swim one stoke and do a basic duck dive, BASIC Blacksmiths can carry out straight forward repairs and make the simplest articles associated with their trade (eg nails, flight arrow heads, javelin heads). Characters with BASIC riding skills can ride a Horse/Pony/Whatever over fair distances without falling off and at a variety of speeds and can control the steed in most normal circumstances.
Characters who are COMPETENT in a proficiency can carry out all of the normal functions of there skill or craft. COMPETENT swimmers can swim a variety of strokes can dive effectively and can swim a short way underwater.. COMPETENT Armourers can make everything but plate armour, COMPETENT weapon smiths can make most weapons (but swords and other weapons with long thin blades are too complex), COMPETENT Blacksmiths can make most simple iron work (including axe heads, hammer heads, spear and arrow heads), they can carryout simple repairs on most types of armour (Sure it doesn't look good but it works). A COMPETENT riders can control a horse in battle, and can use up to size M, one handed weapons in combat while mounted, the character can jump off of the horse easily and can Jump the horse over obstacles.
MASTERS can carry out all of the most intricate activities
associated with their trade. MASTER swimmers can swim any stroke you
have every heard of, they can rescue people as lifeguards do, they
can perform fancy dives, they can swim a long way under water.
MASTER armourers can make any armour (and are the only people who can
make armour good enough to ensorcell), MASTER weapon smiths can make
any weapons (and are the only people who can make weapons good enough
to ensorcell). MASTER riders can do all the things it says in the
PHB
Skill Families
Some skills are related, the most obvious being Blacksmith, Armourer and Weapon Smith, and there is a degree of crossover in these skills. There is a separate document describing the relationship between these three skills. The other area where crossovers are common is Language and again a separate document defines how languages relate to each other.
Non Weapon Proficiency SRs
Most times a proficiency is used a skill roll is not required - the competent blacksmith can always make plough shares, some days it might take longer that others. However sometimes we all try something that isn't really within our ability or in really trying circumstances, in these cases a Skill Roll must be made. SRs are also calculated differently to allow for the skill levels that were discussed earlier. When the first slot is spent on a proficiency:- the player takes one third of the Ability (,ounded to the nearest whole number) that relates to the proficiency (as per PHB etc) adds 4 and then modifies by the Modifier shown in the PHB. It sounds complicated but it is quite straight forward really, as is shown in the example of Peter McTavish. As a first level Fighter, Peter has 3 Non weapon slots to spend, and he chooses to learn Charioteering, Animal Handling and Cooking
Str Dex Con Int Wis Cha --- Peter McTavish ----------
15 - 10 - 10 - 11 - 9 - 13 Oerth Human Fighter L 1
Charioteering is based on Dexterity 2 (according to the PHB) so Dex over 3 = 10/3 = 3.33 rounded = 3. Add 4 (as per house rule) = 7. Modify as per PHB 2 = 9 Basic Charioteering Skill Roll = 9
Animal Handling is based on Wisdom -1 - - so Wisdom divided by 3 = 9/3 = 3 (a whole number so no rounding required). Add 4 (as per house rule) = 7. Modify as per PHB -1 = 6 Basic Animal Handling Skill Roll = 6
Cooking is based on Intelligence with no modifier. So intelligence divided by three = 11/3= 3.66 rounded = 4. Add 4 (as per house rule) = 8. No Modifiers Basic Cooking Skill Roll = 8
Every time an extra slot is spent, not only does the character increase a proficiency category (ie basic to Competent) but the SR goes up by 2. Peter McTavish gains experience and goes up levels, as he does so he GAINS an extra proficiency slot which he spends on charioteering. His skills are now
Competent Charioteering Skill Roll = 11 - he can drive a chariot at a rate 1/3 faster than a chariot driven by a non charioteer in normal and combat conditions. Can launch small hurled weapons at the enemy while driving the chariot single handed. Basic Animal Handling Skill Roll = 6 - Can harness and care for Chariot, Draft and Pack horses, ponies and mules. Basic Cooking Skill Roll = 8 - can prepare and cook basic vegetables and meats, stews or grills the food.
Peter needs to make a skill roll for activities not described above.
Acquiring Non Weapon Proficiency Slots
These rules change the scope of some of the non weapon proficiencies quite dramatically. In the case of Armourer and Weapons Smith the change is certainly in favour of the PC, although with proficiencies such as Swimming and Riding the shift can be seen as detrimental to the PC. Characters are allowed one extra non weapon proficiency slot when they reach level 2 to help redress the balance.
Learning Skills
If you tell me which skill you are practising (and who your teacher is), the level before you gain the slot, assuming everything squares up, you can have the skill immediately it becomes available. If you change your mind about which skill you want we can work out an appropriate learning rate based on that used for languages.