I have a very simple question. I would like to know whether when writing Italian it is best to include a space after the apostrophe or not.
The apostrophe must not be followed by a space (and it's better avoiding breaking a line at it, if not under severe constraints like typesetting in narrow columns), except in a few cases where, by historical reasons, it marks troncamento instead of elisione. The cases are
(possibly some others that I can’t remember now).
The last three can be also written veh, toh and beh (see, for instance, To’ o toh). It would be incorrect writing these words with an accent (but it can be seen, unfortunately).
The apostrophe can be preceded by a space, but this is seen only in poetry (where other cases of truncation marked by the apostrophe, so followed by a space can be found, here the reason is metric):
Allor fu la paura un poco queta
che nel lago del cor m'era durata
la notte ch’i’ passai con tanta pieta.
E come quei che con lena affannata
uscito fuor del pelago a la riva
si volge a l’acqua perigliosa e guata,
così l’animo mio, ch’ancor fuggiva,
si volse a retro a rimirar lo passo
che non lasciò già mai persona viva.
Poi ch’ei posato un poco il corpo lasso,
ripresi via per la piaggia diserta,
sì che ’l piè fermo sempre era ’l più basso.
(Inferno, canto I, 19–30)
A different case is that of the imperative forms
where the apostrophe actually denotes neither truncation nor elision; these are alternative forms to dai dici fai stai vai that developed along with them. The apostrophe here is just an orthographic convention. Also these forms should have a space after them (unless, of course, punctuation follows).