"I need to get a new passport."

Translation: Jag behöver få ett nytt pass.

[Krizelfo]

When do you use 'att'?

[Yerrick]

Some verbs need to put "att" between themselves and infinitive-form verbs; it is based only on the first verb. But there's no pattern, you just have to remember which verbs need "att" after them.

[LelandSun]

Zzzzz's posting on this thread gives very helpful guidance in this regard.

[Berniebud]

Can "Skaffa" be used here?

[Arnauti]

Yes, that would be fine. Jag behöver skaffa ett nytt pass (or skaffa mig). That will focus on the process of trying to get the passport, rather than on the result as få does. But get in English is ambiguous here, it has both those meanings.