To improve a Tradeskill, use it. As long as an item is still challenging for you (i.e., near your Tradeskill level), you’ll improve as you craft it. Each item made by crafting boosts the skill (up to a certain limit that is determined by each item). The number of points earned from making an item varies based on the length of time required to make it, value of the components, etc.
Anyone may craft using any Tradeskill, and skills cap based on the character’s Intelligence and Perception stats, so players who spend AP on those will get further in crafting than those who spend AP on other things.
Note that because crafting consumes a fair amount of real time, it will be a challenge for any one player to max out every Tradeskill. Facilities reduce the time required to craft an item by as much as twenty-five percent. Such facilities can be found in many settlements and are denoted on your Tactical Map.