L'insegnante scrive una parola nuova sulla lavagna.

Italian articles la (feminine singular definite) and una (feminine singular indefinite) drop the final vowel when the following word begins with a vowel, to avoid a vowel clash (hiatus). You replace the dropped vowel with an apostrophe.
• la insegnante → l’ + insegnante = l’insegnante
• The same happens with una amica → un’amica

The noun insegnante ends in -e and can be either masculine or feminine. The elided article l’ originally stands for il (masculine) or la (feminine), but you can’t tell gender from l’insegnante alone. Context usually clarifies, or you might add adjectives/pronouns:
• Il / la mia insegnante
• L’insegnante maschio / femmina (rarely used)

Scrive is the third person singular present indicative of scrivere (to write). In Italian the simple present covers both the English “writes” and “is writing.” If you want to stress that the action is in progress right now, you use the periphrastic present continuous:
• Sta scrivendo – “(He/She) is writing.”

Many descriptive adjectives (like nuova) typically follow the noun in Italian:
• una parola nuova
However, you can also say una nuova parola without changing the basic meaning. Putting the adjective before the noun often adds a slight stylistic emphasis or personal nuance, but both word orders are grammatically correct.

Sulla is the contraction of the preposition su (on) + the definite article la (the). Italian prepositions di, a, da, in, su routinely combine with articles:
• su + la = sulla (on the)
• su + il = sul, su + i = sui, su + le = sulle, etc.