Credere is a very common verb. It basically means "to believe," but not 100% of the time. There are some sfumature (nuances) to this verb, and it so happens that in a recent episode of Sei mai stata sulla luna, it's used in 2 ways that deviate from the norm.

Non ti credere

In one scene of the segment of Sei mai stata sulla luna, we see a single father (Renzo) having a conversation with his son. His son wishes he had a mother, and Renzo is downplaying it.

It plays out like this:

No, per starci insieme.

No, to be together.

-Ma perché non stiamo bene insieme io te?

-But aren't we fine together, you and me?

-Sì, ma magari staremmo meglio.

Yes, but maybe we'd be even better.

-Non ti credere, eh.

-Don't be so sure, huh.

Una fidanzata ti manderebbe tutte le sere a dormire presto.

A girlfriend would send you to bed early every night.

Captions 38-42, Sei mai stata sulla luna? - film

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Come crede/come credi

At the beginning of the segment, the townsmen are hanging out in the piazza and Guia is there, too. Someone says to her, being polite:

Comunque, signora, Lei faccia come crede.

In any case, Ma'am, you do as you think best.

Caption 1, Sei mai stata sulla luna? - film

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If it were an informal situation, it would be fai come credi. It can mean "do as you think best" or "do as you wish." It's often said when there is a disagreement about what to do or how something should be done. The person who says it doesn't think it's a particularly good idea. It's a little different from, fai come vuoi (do as you like), where the verb is volere. Credere gives the person a bit more credit for thinking things through. Fai come vuoi  (or in the polite form faccia come vuole) can also come off as judgmental, depending on the tone with which it is said. 

A variation

A common variation on this expression is with the verb parere (to seem, to appear):

Noi ci sposeremo e soprattutto divorzieremo.

We'll get married and above all we'll get divorced.

Tu stasera vai in albergo, da tuo fratello,

This evening, you will go to a hotel, to your brother's,

dove ti pare, lontano da me.

wherever you want, far from me.

Captions 32-33, La Tempesta - film

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Note that parere is one of those verbs, like piacere, where the subject is not the person doing the liking or the wanting. So, thinking literally, the gist would be "go where it seems to you that you should go." 

Dove ti pare is a very common way to say dove vuoi (wherever you like).

Come ti pare is a very common way to say come vuoi (however you like). 

It's interesting that both parere and piacere are also commonly used nouns: il parere and il piacere. 

Parere (both the noun and the verb) come from the verb apparire (to appear, to emerge).

For more about piacere see this lesson:

and see this video:

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