Talent is natural, and inherent. It can be enhanced, or wasted, but it can't be created from nothing... though sometimes talents in one area can transfer, at least somewhat, to a closely related area. Talent can, to some extent, compensate for a lack of skill.
Skill is learned, through training and instruction. Skill can be taught from nothing, though without any natural ability, it will be much harder to do so. As with talent, skill in one area, can, at least somewhat, transfer to a closely related area. Skill can, to some extent, compensate for a lack of talent.
Experience is earned, through the application of skill and talent, over time, and through trial and tribulation. Experience in one area is often applicable to many other areas. Experience can sometimes compensate for a lack of skill or talent, but NOTHING can compensate for a lack of experience.
UPDATE: Several commenters have suggested additional elements such as charisma, luck, hard work etc... While these are certainly important, they are not elements of competence... They are however elements of success... as is competence in fact.