Historically, English, French, Spanish, Portuguese, Italian (and who knows which else), languages that use the latin alphabet, do many elisions, i.e., supression of letters (and sounds, therefore). This phenomen is marked by the apostrophe.
But the English usage is mainly noticeable when a vowel in the middle of the word (that is, not the last letter) is supressed.
e.g.
Do not - Don't
Friendes - Friend's
On the other hand, the Romance languages usually supress letters when two vowels (they don't need to be the same) of different words meet each other.
e.g.
De água or Da água - D'água
Le arbre - L'arbre
De Alcañiz - D'Alcañiz
Questo orologio - Quest'orologio
Spanish and Portuguese hardly use the mark anymore, but, nonetheless, the words are very commonly linked in spoken language. French and Italian still use the mark a lot.
As far as I've been taught, the rules for the Italian indefinite articles are the following:
Masculine
Un (before words that begin with consonant or vowel)
Uno (before words that begin with s impura, x, z, ps, gn...)
Feminine
Un' (before words that begin with vowel)
Una (before words that begin with any consonant)
Then:
"(Io) sono un insengante" (m., vowel)
"(Io) sono un infermiere" (m., vowel)
"(Io) sono un dirigente" (m., consonant)
"(Io) sono uno psicologo" (m., ps)
"(Io) sono un'insegnante" (f., vowel)
"(Io) sono un'infermiera" (f., vowel)
"(Io) sono una dirigente" (f., consonant)
"(Io) sono una psicologa" (f., consonant)
Despite the lack of apostrophe, "un" before vowels is mainly pronounced linked with the next word, just like the feminine version with apostrophe.
At last, the default for words ending in -ante, -ente, -inte is to have the same form for masculine and feminine. But there are tons of "exceptions", so it's better to learn word by word.
Cf. studente-studentessa, in Italian, and presidente-presidente-presidenta, in Portuguese and Spanish.