My question is what verb should I use in this sentence, The president of the college, together with the deans, (is)(are) planning a conference for the purpose of laying down a series of regulations. Could you please educate me on the rule of why it should use is or are?
“Additional” phrases like accompanied by, as well as, in addition to, along with, and together with are not a part of the subject and do not affect the verb. The verb should agree with the subject:
The president of the college, together with the deans, is planning a conference for the purpose of laying down a series of regulations.
Sometimes a reconfiguration can yield a more euphonious sentence:
The deans, together with the president of the college, are planning a conference for the purpose of laying down a series of regulations.
The general rule is that if the subject is singular you use "is" and if the subject is plural you use "are". You probably know that but are unsure because of the additional clause.
So here's a second rule: Explanatory clauses like this are not part of the subject.
When in doubt, it is often helpful to strip out extra clauses and see what you have left. In this case, "The president is/are planning a conference." The subject is "president", so the verb should be singular, "is planning".
Note that you could reword the sentence to mean essentially the same thing but converting that clause into part of the subject. "The president of the college and the deans are planning ..." At that point the subject is "the president and the deans", which is clearly plural.