The most general Italian verbs/phrases to convey the sense of “to need” are avere bisogno (di) and occorrere. For instance, “I need help” is Ho bisogno di aiuto or Mi occorre aiuto. The latter is less colloquial, more literary than the former.
Another way to say this is with the impersonal use of the verb servire; so, the above example could also be translated as Mi serve aiuto. In a sense, avere bisogno emphasises the actual need, while servire borders on “I could use [whatever]”.
Some uses of “to need” are better conveyed by a colloquial construction with the verb volere. To say that to make some cake one needs two eggs, you might say Per quel dolce ci vogliono [but also servono] tre uova. Or ci vuole un bel fegato for “it takes a lot of guts [to do something]”.
Necessitare is more along the lines of “to be in need of”, but it sounds presently quite affected. Note that in modern Italian (and in this meaning) it is usually constructed with di: so, for the previous example, Necessito di aiuto. Essere necessario is somewhat more usual, especially in regulations and the like: È necessario inserire la password (“You have to insert your password”).
Finally, the main meanings of impiegare are parallel to those of “to employ”, both in the “give work” and in the “make use of” senses. It may be used in a vaguely similar sense to the “need” meaning, in sentences like Il treno impiega tre ore per arrivare a Firenze, that is, “It takes three hours for the train to reach Florence” (but most people, in ordinary speech, would probably say Il treno ci mette tre ore).
For further nuances about some of these terms, the Dizionario dei sinonimi by Niccolò Tommaseo is as always enlightening, even if it is about 150 years old. For the present topic, who desires to strike out into 19th-century Italian will be rewarded by reading here.