Experience and Character Improvement
These things tend to happen in the sequel, if there was one, which there isn't. So there are no hard and fast rules for it.
However, a film might involve the characters learning things; not just about themselves, but new skills as well. Whether this happens depends solely on the story. If a training sequence (or a moment of spiritual revelation) appears in the film, or the GM decides there has been a significant learning experience, the GM may award the PCs one or two character-building points. Costs remain the same as for character generation, but see below for raising the Matrix stat.
Secondly, many people are probably going to want to run a game involving a PC or PCs coming out of the Matrix. Give such starting characters a Matrix of 1 and one skill at Expert and that's it. Then, hand out building points as the game goes along as above. Again, let drama be your guide: after a significant action scene or dramatic moment of discovery, grant them another stat point. In a five-act story, this is one after each of the first four acts, giving you a complete PC just in time for the final showdown.
In both cases, improving the Matrix stat should be more difficult than simply raising a skill, and requires more significant events to justify it. Players must really work hard to raise their Matrix stat, as it means reaching a new plane of understanding and control. Only when they face their fears, go beyond their limitations, and do what they thought they could not do, do they prove themselves ready for such an increase.
Example:
Neo enters the lobby of the Agent building with a Matrix of three. After this insanely dangerous battle, he gains a Matrix point (when he says "There is No Spoon"). On the rooftop, he puts this to good use, and dodges bullets, then catches a helicopter in his bare hands. Morpheus walks up to him, claps him on the shoulder and tells him that knowing the path is not the same as walking the path. Neo gets another Matrix point. Technically, he shouldn't have been able to dodge bullets yet while still at level four; it was in trying it anyway that he learned how to do it.