- very (when used with an adjective)
- considerably (when modifying a comparative or verb)
- much (when modifying a comparative or verb)
You can see the adverb used in its context below:
I ricercatori credono che i nostri comportamenti siano assai più prevedibili quando siamo al ristorante e scegliamo cosa mangiare. (read the news story here)
Researchers believe that our behaviors are considerably more predictable at restaurants when we choose our dishes.
In the example above, it's modifying a comparative (più prevedibili).
Here's an example of assai modifying a verb:
Ho mangiato assai in vacanza. Adesso devo tornare in palestra per dimagrire un po'.Here's an example of assai modifying an adjective:
I ate considerably on vacation. Now I have to return to the gym to lose a bit of weight.
Ho tentato di spiegare bene il problema ma purtroppo è assai complesso.
I attempted to explain the problem well, but unfortunately it is very complex.

