«The subject is usually not explicitly said» is an overgeneralisation. Of course the subject has to be mentioned at the very least the first time something new is mentioned, and then again, especially if several things or persons are mentioned.
It is not easy to give an answer about the position of the subject that is good for any possible situation: very much depends on the wider context (the sentences before and after, who is talking/writing to whom etc.), but as a very first approximation:
“Scrivo” is the most neutral way of saying that I write.
“Io scrivo” is a more assertive way of saying it, perhaps to say that it is your profession (“Io scrivo: so bene come usare le virgole”) or to stress that you are going to write something no matter what. The emphasis here is on scrivo.
“Scrivo io” is the least usual of the three, and would convey the sense that it's better that I am the one doing the writing. For instance, you are making too many mistakes, or losing time, so give me the pen and scrivo io. The emphasis here is on io.
Mind that, in other situations, the subject after the verb may be way less marked, and sometimes is almost the only way: «“[Some statement]”, ha dichiarato oggi il ministro», «“[Witty aphorism]”, come usava dire Oscar Wilde», «C'era un volta un re».
(See also this previous question and its answer.)