Firstly there are two kinds of course entry at TAFE - direct enrollment, and course application. The deadline for course requiring an application are long gone( for those courses look
here), however if you still want to get into an application course then call the campus at which you desire to do your course and enquire after any vacancies they may have.
If you are looking into a direct enrollment course(ie one
not on the above list) then go to the information day for that course and enroll on the spot. To see when the information day is, go to the local campus website(not the main one) for your course and they will have the specific day. It is also important to note that many courses require interviews or placement tests or portfolios so make sure you are prepared for such an occurence.
Hope that helps
EDIT: Oh, and as far as the main TAFE site goes it is rather crap for specific course details - just go direct to the campus site and it'll be more specific about the Cert 3 stuff.
This is the site of the wollongong campus which if memory serves me is the one nearest you.