My infos may be a wee bit out-of-date, some rulings having been changed recently, but I can't leave this post unanswered.
What do you mean by handymen? My dictionary gives 'Hilfskraft' which is not what the Swiss would call themselves when doing a four year apprenticeship. Nor would they call it 'learn a job and earn some money'. The 'rate of pay' for a first year apprentice is nowhere near enough to live on.
Firstly, a school-leaver must find a firm which will take him on as apprentice. This often means working for various firms, writing many job applications and attending interviews. Having acquired this place, the more academically minded apprentices may be able to study for the Berufsmatura parallel to their work in the firm, enabling them to go to the Fachhochschule (technology, social and natural sciences and art) afterwards. Until the last couple of years, when the Matura (and often a University Education) became the requirement for professions where previously aptitude was considered more important, a good final examination after four years apprenticeship and a good employer's reference was the gateway to a worthwhile and life-long career in a trade and carried with it the respect it deserved.