I’m an administrator in a grad. program. My stock advice to prospective applicants is to write to the professors they’d like to work with, sending a brief note and a CV. But I also advise applicants not to take it personally if they don’t get a response, because faculty are inundated with requests and many prefer not to interact until they can see the entire application, in the context of other applications. To the question of whether a particular professor is accepting new students; unfortunately, that’s not a question we can answer this far in advance, at least at my school. We’re only allocated so many funded spots by the school, and that number can vary a bit from year to year, and we don't get that number until after applications close. In addition, some faculty won’t decide whether they want to admit anyone until they can review applications. If they decide against it, their funded new admit slot may float down to a professor who’s next in line. I tell applicants to apply to work with the faculty with the best match of research interests, and hope for the best.