Characters study and practice their skills in order to improve. Each character is able to work on learning 3 new skills at any one time, a number that is modified by the character's INT resistance modifier. (A character with an INT of 11 would be able to train in 4 skills at a time).

Training in a skill is a complex skill test in that particular skill. If the character does not have the skill, then her test is made using the broad skill for that specialty skill (don't forget the +1 penalty for using a broad skill). If the character is trying to learn a broad skill, the test is = the appropriate attribute (still w/ +1 penalty) as if she were trying to use the skill without training

Teachers and tutors help a great deal (see below), but are required only for the initial skill level in skills which cannot normally be used untrained. (GM's may make exceptions to this if the character has some other resource for the skill -- a good manual or videos of "This old house", a "Complete Idiot's Guide to", etc.). Once the character has the initial training in the skill, he may strike out on his own and try to advance without a tutor, but of course that will be much more difficult.

The number of successes required to earn the new skill is equal to the number of skill points that level of the skill would cost (using the original skill point cost rules, not the optional rules). Characters may take a roll to advance in that skill once per week, and at the GM's discretion when the player rolls an amazing success with that skill.* 

[*To offer this at every success would be a bit too much for combat skills in a combat-heavy game. It's tempting to overcomplicate this, to require that the tests be of at least a certain difficulty, so that characters won't get these advances for point blank shots at sleeping victims, but that's too much. If we leave this to the GM's discretion as the game is played, that's a bit simpler. I would recommend that for most skills, if the test was taken at average or greater difficulty (+d0 or greater penalty) then the GM should allow the advance roll on the complex test.]

At the end of a week of study (or after an approved amazing success) the character makes a roll on the complex skill test to learn that skill. 

Result of Learning test roll:
Critical failure = fail test completely, start learning from scratch
Failure = nothing (three failures fail the test completely, start from scratch)
Ordinary = +1 success
Good = +2 successes
Amazing = +3 successes

It is not necessary for the character to actively dedicate time to the practice of the skill. We can assume that the character is practicing and learning in off times - reading before bed, some practice moves in the mornings, etc. As an option, the GM may apply condition modifiers to the tests - obviously a character sitting around a university library is going to have a better chance developing a INT skill than will a character who is on the run from the law, hiding out in sewers. The conditions will be at the GM's discretion, and should be evaluated on the whole for a given week - one day on the road doesn't make it terrible conditions all week for more academic studies, etc. These conditions should be evaluated based on the setting and the requirements of the individual skill. The university library is a good or amazing place to study an ancient language, but it's a terrible place to learn to track deer.

Modifiers:

Peer:
Studying with a partner (must have a skill level + or - 2 of each other) = -1
(This bonus can only be taken once - additional peers do not help)

Level of Skill:
(Higher level skills are more difficult. In addition to the greater number of successes required, the tests get harder as the levels go up)

Media (bonuses for media may be combined with other bonuses, including teaching bonuses):

A book on the subject = -1
Media on the subject (video, film, holos, tapes, etc) = -2
Completely interactive computerized instruction (AI or something close to it) = -3

Note: books and other media usually are only useful for a particular range of skills - usually one broad skill, or three levels of a specialty skill.
Media that apply to higher levels are more rare. If you want to randomize that determination, try this table:

Doubling up:
A character that wants to focus more intently on a particular skill may devote more than one learning slot to that particular skill. At each point that the character would be allowed to make that roll she may take one roll per dedicated slot, and may use the best result she rolls.

Teacher Modifiers:
Using a teacher has two effects on the skill test. To begin with, the teacher provides a bonus depending upon how advanced his skills are in the skill he is teaching. In addition, the teacher must make a roll on his TEACH skill for that particular skill (note: if the teacher does not have the particular teaching specialty skill, use the broad skill. Don't forget the +1 penalty).

Being a Teacher:
A character that is teaching a student a particular skill must devote one of his learning slots to the teaching specialty skill while he is teaching. While teaching the teacher has the opportunity to improve on his teaching skills. Every time a student successfully completes a skill level, and for amazing success a tutor rolls while tutoring students, he may take a roll on the complex test to improve his teaching skill. For this test, use all of the same modifiers as the basic complex learning test (including those for the tutor having a teacher of his own, a book or video on teaching techniques, the conditions under which he is giving the instruction, etc.). Also note that if a tutor has several pupils studying the same skill, he makes the test only once for each "class", not for every student, and only once every student in the class has completed the level. 

In this way, someone who has no teaching skill but high Power Martial Arts skill would gradually learn about teaching, getting better the more she teaches. 

Example

All right, for your reading pleasure, here's an extended example of the skill advancement rules in action. The one thing I have not tried to demonstrate here is the extra rolls a character gets when he gets an amazing success using the skill he is training with -- trying to simulate that would be too tricky. So here's a week-by-week example of about three months in a character's learning curve . . . I sat around and did all these rolls myself, and the results of the case study are interesting, and illustrate some interesting points of the system. 

Sorry this is a little long, but I thought it would be interesting to try out the system.

Hiro Protagonist (with apologies to Neal Stephenson) is a young combat spec. ( s11 d12 c9 i9 w11 p8) with these skills (among others): Unarmed Attack-power martial arts-1, Ranged Weapons-rifle-1, Knowledge-first aid-1. 

He has selected three skills to study: power martial arts-2, pistol-1, and first aid-2. He has a teacher, Gomer Pyle, who has PMA-4, pistol-3, and the Teach broad skill (and one level in the appropriate specialty skills to teach pistol and PMA). He has a video on first aid, which provides instruction for basic first aid (levels 1-3), and the facilities to watch the video.

Gomer's teaching tests will be (12/6/3 -- he has an 11 will) and at +0 

Hiro's PMA test will be (12/6/3) and be at +0 because he has a tutor with the 3 level advatage on him. Gomer's success on his teaching roll will modify this roll. He needs 5 successes.

Hiro's Pistol test will be (12/6/3) and be at +1, because he has a tutor with a 3 level advantage, but he is using the broad skill Ranged Weapons to learn the first level of this skill. He needs 4 successes. 

Hiro's First Aid test will be (10/5/2) and be at +1 (+3 because he has no tutor, and -2 because he has a video). He needs 3 successes. 

Week 1
PMA- Gomer rolls 2 (amazing). Hiro's test is now at -3. Hiro rolls 15-5=10, ordinary success. (1 success-0 failures).
Pistol- Gomer rolls 7 (ordinary). Hiro is now at +0. Hiro rolls 20, critical failure, Hiro must start from scratch.
First Aid - Hiro rolls 19+3=22, fails (0-1)

Week 2
PMA- Gomer 10 (ord.) Hiro at -1. Rolls 4-4=0 (amazing) (4-0)
Pistol - gomer rolls 8 (ord.) hiro at 0. Rolls 12 (ord.) (1-0)
First Aid - Hiro rolls 7+4=11, fail. (0-2)

Week 3
PMA - Gomer 18 (fail) Hiro at +0. Hiro rolls 5 (good) so (6-0) Level Earned.
Pistol - Gomer 3 (amazing) Hiro at -2, rolls 4-6=-2, (amazing) so (4-0) level earned.
First Aid - rolls 1+1=2, amazing (3-2) level earned.

Lucky Hiro has earned all his levels, decides to continue to work on the same skills Here are the new tests:

PMA - Gomer may no longer be Hiro's tutor, as he no longer has a 3 level advantage. Gomer is interested in developing his own skills at PMA, so will work with Hiro as a peer. Hiro's tests, then are (13/6/3) and he is at (+3-1) +2. He needs 6 successes Pistol - Gomer may no longer be Hiro's tutor, as he no longer has a 3 level advantage, and Gomer is not interested in more practice on pistol, so Hiro is on his own. His tests are at (13/6/3) and he is at +3. He needs 5 successes. First Aid - Hiro is still able to use the video for one more level, so his tests are now (11/5/2) and at +2. He needs 4 successes. 

Week 4
PMA - Hiro rolls 13+2 (fail) (0-1)
Pistol - rolls 12+2 (fail) (0-1)
First Aid - rolls 2+2 (good) (2-0)

Week 5
PMA - rolls 5+4 (ord) (1-1)
Pistol - rolls 8+6 (fail) (0-2)
First Aid - Rolls 15+3 (fail) (2-1)

Week 6
PMA - rolls 10+3 (ord) (2-1)
Pistol - rolls 1+5 (good) (2-2)
First Aid - rolls 11+2 (fail) (2-2)

Week 7
PMA - rolls 18 + 5 (fail) (2-2)
Pistol - rolls 11+1 (ord.) (3-2)
First Aid - rolls 15 + 2 (fail) (2-3; fails learning test, successes are lost)

Week 8
Hiro has decided to forget about the First Aid stuff for a while, and double up his concentration on his Pistol training.
PMA - 12+1 (ord) (3-2)
Pistol - 11+5; 12 +3. best result is Fail. Progress is wiped out.

Week 9
Hiro is frustrated, and decides to focus all three slots on PMA. PMA - 2+6; 10+3; 8+2. Best result is ord. (4-2)

Week 10
PMA - rolls 19+2; 4+3; 3+6. Best=ord. (5-2).

Week 11
PMA - rolls 3+3; 11+5; 10+5 best = good (7-2) level earned.

I'll stop there. So after 11 weeks of training, Hiro has earned two levels of Power Martial arts, and one level each of First Aid and Pistol. 

Here's what I think this shows us:
1. How much help having a teacher is -- the twofold advantage of the teacher's skill test modifying a character's learning tests, as well as the basic modifier for having a teacher. As much help as books and videos are, they don't get the additional test to help a character learn. 

2. How important it is to be able to focus two or more slots on learning one skill -- otherwise characters working to learn in adverse situations, without a teacher, etc., won't have much chance of learning anything.

Therefore, GM's who are concerned that this system allows characters to advance too quickly, as it may appear Hiro did in the first three weeks (he was REALLY lucky, but still . . .) can exert controls on the availability of teachers and media for the characters, and in that way limit the rate at
which they advance. Also, GM's who feel like this is too easy could also throw in condition modifiers that reflect the amount of time each week the character is actually spending on learning the skill -- from all day training (-3) to not thinking about it at all (+3) and all the gradations between. For characters that are actively adventuring, that should slow them down a great deal.

GM's who feel that this system is too slow, should first remember that there will be extra tests now and then for amazing successes, and also consider removing the three strikes rule -- the rule that states that if you fail the complex learning test three times you fail the test completely and must start again from scratch. That way characters will only loose their progress when they roll a critical failure.