Quick question: the manual doesn't mention experience points, promotions, increasing skills or anything else on character development.
What's your suggested approach here?
This is all covered in Chapter 11.1, in the Resolution sub-section. Like most things in the GM section, it's admittedly (though purposely) a tad vague.
The method recommended there for increasing skill points is for the GM to award players skill points for critical successes and to
consider skill deductions for botches (actually, it recommends the deduction but I've had five years to consider this and depending on the attitude of your players it may not be the best of ideas; certainly makes sense, though). Promotions are another potential reward for an adventure/mission, though those are completely up to the GM's discretion, and gaining Talents or Complications (or mitigating them) falls along the same general lines. The game doesn't use XP; in my research prior to SFRPG's development (WCRPG's immediate antecedant), I came across several RPG systems that don't use them as part of their mechanics.