The way to enroll for an apprenticeship program is to find a job. You have to look for an employer in the field you want to apprentice in. You go there and say you are interested in apprenticing. If they are interested in hiring you, they may either offer you a full time job as a helper to try you out with the intention of signing you up for an apprentice after a couple of months if you turn out to be reliable or they may even sign you up as an apprentice right away. You will in any case have to give up your current factory job to work full time for this employer and most likely for better pay as well.
The employer is then obligated to teach you the trade. In the beginning, you may be helping out with mundane tasks but bit by bit, they will teach you things you need to learn for the trade. Some trades take 3, others 4 years to apprentice. In some of them, you spend 2 months a year in school, in others 3. You will have to research that for the particular trade you are interested in. After completing your first year of work experience, you should look into registering for the school part. You will of course have to ask your employer when it suits them to let you take time off for school. During your school, you will get EI (you will of course need to apply for it). During your school, you will do shop training as well as possibly some math, drafting etc. You will take exams and do projects. After you have completed your first year school, you return to your job as a 2nd year apprentice and get your payrise because you are now capable of more tasks and more valuable to the employer. Repeat that for as many years as the apprenticeship takes and you will become a journeyman, take the red seal exam and be qualified to work as a journeyman in your trade in any province.
You can look at training standards in Ontario here: http://www.collegeoftrades.ca/membership/resources/training-standards and here you will find some info as well: http://www.tcu.gov.on.ca/eng/apprentices/app_train.html
The one year course you are talking about would be known a pre-employment training and it not actually necessary in order to apprentice. I took a course like that and it did not really get me a head start. I spend 8 months in school, full time (one school year) and for it, I got credit for the 2 month first year school for my apprenticeship. During the time I had entered my pre-employment program, there was a lady who started working directly for the same employer I ended up with as a first year apprentice. Of course I did not meet her until I started working there but during the time I was in school, she was working and making money and later she did enter school and complete the 2 months of first year school that I already took during my pre-employment thing. However, me spending 8 months and her 2, she was still 6 months ahead of me with work experience towards her apprenticeship and she had 6 months of income that I didn't have because I was in school. Besides, I did not qualify for EI while I took my 8 month program which she got during her 2 months program. You see that by taking that year, I did not get a head start. Actually, she had a head start on me. Therefore, I don't recommend that you do that unless you have difficulty getting a job in the first place. If that is the case, then go ahead and take the year because it will help you get your foot in the door but only for that reason.
You can not be overqualified for an apprenticeship. You just say you are changing careers if anybody asks. I met quite a few people who were apprenticing who had university degrees before doing an apprenticeship.