What is correct English? What does it mean to speak correctly? Very simply, correct language usage is that which conveys to your intended audience the impression you would like to give them. If your readers or listeners are college professors or academic colleagues, the appropriate language is a fairly formal variety of Standard English (SE). The deference due to business contacts and clients also merits a fairly polished level of language usage, while other environments may demand very different modes of communication.
This preferred SE language standard (See Prof. Lynch's discussion of Standard English) is associated with educated speakers of the language and, although there exist minor differences between the SE of different regions and countries, in most cases these are minor spelling or pronunciation variations which do not in any way interfere with comprehension of written material from one English speaking country to another. In all important respects, there does exist a universal English standard.
The vast majority of English grammar and style rules encountered when taking English lessons are not in dispute. Those targeted by standard exams such as the SAT and others are deserving of study and close observance. Although breaking rules may well be an appropriate device to use from time to time for emphasis or effect and has certainly been done extensively for that purpose by many great literary figures, one must always consider what impression such infringements will give one's readers. In general, failure to break a rule rarely results in criticism or gives offense, while the commission of an infraction may. If one does not know one's audience well enough to rule out the possibility of a negative response, it is probably best not to risk provoking one.
Some common grammar rules are questionable and indeed the arguments in favor of some commonly eschewed usages have been convincingly refuted. However, the audience-impression argument is still the ineluctable determinant of expressive suitability. If there is a likelihood that a split infinitive, a synesis error, or use of "none" as a plural noun may be perceived as an error (whether or not this perception is nonsense), it is simply better to avoid the usage in question.
An online English class that follows these principles is available.