If a student was accepted for admissions with the college through a special program the college offers but a student wants to be accepted for regular admission what steps should be taken and with whom?
Question is too vague to answer. What do you mean by speical program? Typically you can be admitted to a college only once per year and usually have no reason to change it. If what you mean is that you were admitted via a binding Early Decision program and now want to withdraw that and flip to being considered for regular admission so you can also see if other universities will admit you, the answer is no. The college may (or may not) let you out of the ED admission decision, but if it does you will not be considered for regular admission.
I was admitted for the freshman transition program at the college.
Freshman transiton program is also a term that has a variety of meanings. If you mean you applied to a college for regular admission and were not offered regular admission but instead a transition program such as (a) starting in summer school at the college before next Fall (one form of transiton program), or (b) attending a community college for a year or two (another form of transiton program), and then © if you meet certain levels of success in either program that you will then be able to enter the university, then likely you cannot get the decision changed, but you may want to find out if the college has an appeal process for those admitted under transition programs and possibly pursue it.
You need to contact the college directly and ask.